Lost registration code

I've lost the registration code to my Sims 3 Ambitions game. It was not registered in Origin when I first downloaded it, due in part to whatever reason 13 year old me had for not downloading it. I recently decided to reinstall all my games, and for most of them I was able to find my registry code along with the disk, but for the case of my Sims 3 Ambitions, I have found that I was unable to find the code, or the box that it came in. I have sitting in front of me the disk, and without the registry code, no way to install it on my computer. I'd rather not pay 20 bucks to buy something I already have a copy of, so I was hoping that someone could either tell me how to retreive the registry code from the disk, or failing in that, tell me what to do, thats not buying another copy.