Air carrier pilot reported during landing at BJX airport they had to avoid a makeshift barrier on the runway. Reportedly; there was no information on the ATIS nor was there a NOTAM advising of the barrier.

Narrative

In cruise; we were preparing for and briefing a landing on Runway 13 at Leon; Mexico (BJX). The current and forecast winds were out of the east. Mexico center informed us BJX was using Runway 31. We requested Center pass along a request to approach for 13. We did not want to land with a tailwind at 6000 feet AGL. Of course Approach ignored our request and gave us Runway 31. Unfortunately with airports in Mexico not having a digital ATIS; and the inability to pick up the current ATIS over VHF until you are on the arrival; you have to try and prepare for landing on either Runway - including briefing the different arrivals; different Runways; different approaches; different taxi procedures; different go-around procedures; different special engine out procedures; separate landing assessments…usually with the threat of significant terrain present for each phase of the arrival and landing. Not knowing which Runway to expect until the last minute makes it very difficult for pilots to feel prepared especially when the NOTAMS are incorrect! With the WiFi active we are able to constantly refresh our App; and get current NOTAMS for the destination airport throughout the flight. At BJX; there was a NOTAM for a displaced threshold for Runway 13 with specific distances available listed for takeoff and landing; but only for Runway 13; including an available landing distance of 3020 meters; approximately 9900 feet. NO NOTAMS FOR Runway 31; and nothing about a temporary barrier on the Runway! With no NOTAMS listed for Runway 31; and nothing on the ATIS(when we could finally hear it) besides the displaced threshold for 13; we assumed the entire Runway length was available for landing on 31. We prepared landing assessments for both Runways; considering the high altitude; winds; and displaced threshold(only for Runway 13). Also; at BJX there are limited taxiways to/from the middle of the Runway; and turn buttons at each end. Our company Advisory Pages state that 180 degree turns on the Runways are not permitted; and company aircraft must use the taxiways or turn buttons at the end of each Runway. During the descent I briefed the First Officer; considering the high altitude and no need to make an aggressive deceleration and make the passengers uncomfortable; we would probably not make the taxiway in the middle of the Runway; so we would simply roll to the end of the Runway and use the turn button. I executed a normal approach and landing to Runway 31. After touchdown I maintained adequate speed to safely and efficiently roll to the end of the 11;486 foot Runway. As I was rolling out; the Tower Controller mumbled something in a thick accent about caution for the displaced threshold." Neither of us knew for sure what he was saying or why; because the displaced threshold was only for Runway 13; according to the NOTAMS. A moment later the FO (First Officer) spotted something ahead on the Runway. There was a makeshift temporary barrier made out of rubber stoppers or cones at the position on the Runway where the displaced threshold for Runway 13 ended. Most of the barrier appeared to be rubber cones; with it containing more substantial materials just off the center of the Runway. I'm not sure if the barrier would have caused damage to the airplane if we rolled over it; thankfully we did not. I was able to stop the aircraft just shy of the barrier; and perform an awkward; company unapproved 180 degree turn; barely missing the barrier and Runway edge lights in the turn. At that moment; turning the airplane around and clearing the Runway was the safest and most prudent option. I did not want to risk taxing over the barrier; and with no Runway shoulder; the feasibility of a tug attempting to reposition the aircraft with the tug's tires in the grass seemed unattainable and could have possibly resulted in a lengthy closure of the Runway. Also; there was a non- US carrier on final. With the language barrier and heavy accents; I didn't want to take the chance of miscommunication resulting in an accident. After exiting the Runway; I tried to explain to the Local Controller the seriousness of the threat to our flight and future flights due to the lack of specific NOTAM information re limited landing distance available and the presence of a barrier on Runway 31! After we were safely parked at the gate; I immediately called Dispatch to inform them concerning the situation at BJX. I also directed Dispatch to pass along the information to the our company pilots taking the airplane back to ZZZ; and any other crews flying into BJX; including any non-company US based pilots. The next morning (XA:15 departure); the NOTAMS had been updated to include Runway 31; and the reduced distances for takeoff and landing. The non-digital ATIS still only included the displaced threshold and reduced distances available for Runway 13. Nothing for 31. Incorrect and lack of important detailed NOTAMS for Runway 31 at BJX airport. Language barriers; and accents. Expectation biasSuggestion: More time; effort; and personnel dedicated to maintaining current and accurate airport information and NOTAMS throughout Mexico. A requirement for air traffic Controllers to be proficient in English. A way to ascertain ATIS and current Runway in use information while still in cruise at a significant distance from the destination airport in Mexico."