It can report that error as "zip code", even if it's something else in the address it doesn't like.
Be sure the state ID code is correct. i.e., AR vs AZ, etc.
Remove any punctuation, such as:
123 S Main St
123 N St Marys Apt 4 (not 123 N. St. Mary's, Apt. 4)
And check what the official styling for the address is at the USPS website below:
https://tools.usps.com/go/TrackConfirmAction_input