B757 First Officer reported that after parking and setting the parking brake; they lost control of the aircraft as it rolled forward approximately 8 feet before the Captain quickly applied the brakes to stop the aircraft.

Narrative

Upon arrival in ZZZ; the Captain stopped the aircraft when signaled by the aircraft marshaller. He set the parking brake and set both engine cutoff switches to OFF. I distinctly remember him doing this because it is my personal habit pattern to physically touch both engine cutoff switches to confirm in my own head that they are off; and I always glance at the parking brake to make sure the handle is up and the parking brake light next to the handle is ON; as I did on this occasion. The Captain called for the Shutdown Checklist; and my eyes went to the overhead panel to begin my Shutdown Checklist flow. As I completed the flow steps on the overhead panel; my eyes went down to the instrument panel and this is when I noticed the marshallers arms waving wildly in the air. I also noticed that the aircraft was slowly rolling forward; and I immediately yelled to the Captain as I began to bring my feet off the floor to hit the brakes. As I raised my feet off the floor; the Captain; who by now had also realized we were rolling; rapidly hit the brake pedals; and my feet fell back to the floor from the sudden shift in momentum. The Captain made a second attempt to set the parking brakes; and we both took a few seconds to make sure that they held this time. The ground personnel had a short discussion and decided to push the stairs up to the aircraft where it stopped. After deplaning; we inspected the area around the aircraft and in the gear well. Thankfully; the aircraft did not make contact with any ground equipment or personnel while it was rolling forward. Also; there was no observable damage to the brakes from our perspective or from the perspective of the mechanic that we spoke to afterwards. Ultimately; the aircraft rolled between six and 8 feet forward of the intended stopping point.Unfortunately; my established habit patterns as a pilot monitoring during parking and shutdown did not suffice to prevent the aircraft from rolling forward on this occasion. In the future; I will pause an extra second or two to ensure that the parking brake holds; and that the engines are winding down as expected. Also; we did not make a write up in the aircraft forms about our suspicion of the parking brake handles uncommanded release. In the future; I will encourage the Captain to do so in such a situation.