Air taxi pilot reported receiving a GPWS terrain warning departing PAJN airport while flying the wrong departure procedure.

Narrative

On Day 0; at about XA15; I received an IFR clearance from Juneau international airport tower to ZZZ airport. Prior to and upon filing my IFR flight plan using the website; I noticed the standard departure I used for the company I flew for; the JNU6 departure was not listed. Instead; I selected a different departure (Asort2) which was preloaded onto the website through our company login. I selected that departure (and later was informed that departure was not authorized for our company using the Garmin avionics). I quickly briefed the departure but did not print it out. I loaded the plane I was to fly; called my one passenger and got cleared for the flight. Another company plane departed minutes before me on a similar route with 500 foot ceilings. I loaded the departure into the Garmin avionics and scrolled through it to make sure everything was in order. Upon take-off; I flew into IMC at about 500 feet and broke out of IMC into VMC at about 600 feet at which time the terrain warning system sounded to; 'Pull up; terrain' for a about one second; then stopped. Because I was now in VMC and seeing the terrain; I didn't fear it would be a factor as I had the warning system; synthetic vision and a visual perspective. At the time of the audible terrain warning; I was in the process of activating the auto-pilot to fly the departure procedure. As I was setting up the autopilot; I noticed the departure procedure showed no turn; only a point that said; 'vectors.' Seeing no continuation on the Garmin for the departure procedure; I deactivated the auto pilot and asked Anchorage Center if I could receive 'vectors' to the next waypoint in the departure. ATC informed me I was on the Asort2 departure and began addressing other aircraft. Based on my recollection of the departure I briefed; it was very similar in nature to the JNU6 departure. I began a right turn and a climb to avoid terrain and went back into IMC at about 1000 feet MSL. I set up the autopilot again to climb at about 700 fpm and made a direct heading to the next waypoint in my flight plan. I was in and out of IMC throughout the rest of my flight and was able to cancel IFR as I neared ZZZ airport; landing without incident. Chain of Events:How the problem arose: I felt rushed to stay on my flight schedule and should have slowed down and asked a more experienced pilot about the departure and instead; use the departure procedure expected of me; the JNU6.Contributing factors: Not taking appropriate steps to realize the dangers of not having a thorough understanding of the departure I used and the weather restrictions involved with the departure which requires pilots to fly at 500 feet to an NDB just west of the airport before continuing to IFR. How it was discovered: Seeing the 'vectors' readout on the Garmin avionics instead of the entire turn listed. Corrective actions: Turning off the autopilot; asking ATC for assistance and hand flying to get plane out of danger. Human Performance Considerations:- Perceptions; judgements; decisions: My initial perception was that the departure procedure I selected would be very simple to fly. Poor judgment in planning. Overconfidence.- Factors affecting the quality of human performance: Not having a full understanding of the departure procedure. IMC into VMC; audible warnings and back into IMC.- Actions: Hand flying the plane back onto course.- Inactions: Slowing down; asking for advice or assistance; requesting the prescribed departure instead of an unfamiliar one.