I think that there might be some merit to @GAS’s proposal. If someone uses codes, he/she is more likely to want to sort the list by the codes rather than by name. If they prefer to rely on names for search and sorting, they probably don’t use codes.
Besides, @lubos once hinted towards the possibility of enabling column selection in tabs:
I don’t know if this is still intended for development, but if it is; this could possibly mean that multifield sorting might be required.