The "auth code" is the code the map gives you. Submit it here and you get a "save code" back, and typing that save code into the map loads your progress.

A code is tied to the StarCraft name it was saved under, so it only validates for the account whose ID matches that name. If you picked the wrong ID when you signed up, go to your dashboard, delete the account, then sign in again and choose the right one.

Auth codes from a modified map, or from an older version of the map, are never registered. Download the current official map above, run it, save, and submit the new auth code it gives you.