A note-it is not necessary to use real world airline codes for 'atc_parking_codes=' in either the airport parking specs or the aircraft.cfg. The sim only needs to find matching codes. But, for uniformity among add-ons ICAO codes are normally used. Also, ATC will not honor the parking codes for your user aircraft, only for ai
Your best resource is probably Afcad 2.21. It comes with a database of the atc_parking_codes commonly used by both FS airport designers and AI traffic authors. Beyond airlines it also contains parking codes for military ai.
Once Afcad is installed you can assign the parking codes from the list to your aircraft using Afcads aircraft editor (Tools>Aircraft editor). You can also check airports to see if and what parking codes are assigned at specific airports, and add or modify parking codes if necessary.
If you're unfamiliar with using parking codes, the Afcad help file (readme.htm) explains it.
At that time  the chief engineer was almost always the chief test pilot as well. That had the fortunate result of eliminating poor engineering early in aviation.