Maybe its only my company or a few trailers we have, but I have seen a big sticker on the inside of the door of the reefer that listed the codes.
C'mon freebird, a Google search for "Thermoking Codes" and this was third choice:
Thermo King Alarm Codes & Fault Codes for Refrigeration Repair : TKX Transport Refrigeration
In all fairness though, this took a little more digging to find:
Carrier Transicold Alarm Codes, Refrigeration Repair : TKX Transport Refrigeration