What are your expectations?
What is the minimum possible that could be done to meet your expectations?
What deficiencies currently exist that are blocking you?
Once you have this written down, only then should you approach the other party. Remember YOU think it is "messy" "lacks docs", however others may think it is fine. You will not win any friends by demanding someone does more work that they don't consider to be worthwhile.
If you have no leverage, then you are asking for a favor.
Be nice, be friendly and courteous. Try to see the other person's viewpoint.
Good luck in your negotiation.