Official Code always displayed on self register
The official code is somewhat specific to certain platforms... and most of the time the users on these platforms (such as educational institutes) will not have the option to self register.
I think displaying this field if it is not required will confuse most people trying to self register.
My proposal is to only display this field on the self registration form if it is required, this way users who don't know what this field means (and probably don't need it anyway) will not be confronted with it from the beginning. The field remains on the account page so if needed it can be supplied, but if not required it is not asked during registration.