Source-aware file
Confirmed material and clearly scoped interpretation only.
Quick answer
The shotgun door code is 4-1-2-3.
Spoiler-light clue
Read the Four Remain file. Its numbers correspond to the descriptions of events in hospital rooms 101, 102, 103, and 104. Match each number to the correct room description before entering the code.
Why this answer is reliable
The sequence and the intended clue route were supplied by a developer reply in the Steam discussion referenced by the keyword research. It is a demo-specific answer; later builds could change the surrounding presentation, so this page will be checked again at release.
Before leaving the area
The door is tied to a weapon-focused puzzle route. Save your current progress first if you want to compare the clue order yourself, then return to the lock when you are ready to use the answer.