I tried this site the other day, it is slow to load so you do need to be patient with it.

There's nothing to sign up for or register. It's affiliated with Audiobook Boom! but you don't need to be a member of Audiobook Boom! to use Freeaudiobookcodes.com but you have to go through their homepage to get there. Audiobookboom.com

The books don't have descriptions so you need to open Audible and look for the synopsis, sample and reviews. If you're interested in the book you select copy code and then redeem code. Once you redeem it, it appears in your library and you now own that book. No review required (although it's nice thing to do, especially if you're listening to a fairly new or unknown author who doesn't really have any reviews yet).

Each title tells you how many codes are available, I search by "most codes available" as my filter so when I hit the books with no codes I know to stop looking.

It's a good way to fill your library if you're between credits or short on funds.