The use of a narcotic, such as Codeine, 5 weeks following any elective cosmetic surgery, including a tummy tuck, is not very common.
In my experience, patients experience the most pain/discomfort within the first 3 days following a tummy tuck.
Assuming that the Codeine is being used for pain, it would be best to identify and treat the source of that pain and eliminate any exacerbating factors, not just simply treat the pain itself. For example, if a suture in the muscle repair has torn through the tissue, an NSAID and/or Medrol dose pack and muscle rest may help.
Narcotic use after surgery can be addicting and should be used sparingly and only for brief periods of time.