TLDR is at the bottom.
PSN game codes (and most DLC codes) can add only 1 game or DLC item to your account. You can't have two copies of "Game A" even though you may try to redeem two different codes for "Game A". The system is designed so that you can't redeem a code for the same version of one game that is already tied to your account, for this example I'm going to use my Blizzard.net account to compare but it is still the same thing as PSN in this regard. I am unable to connect my Collectors Edition of Diablo 3 Reaper of Souls to my B.net account because I had pre-purchased the Digital Deluxe edition several months before launch and hadn't expected to get my hand on a physical copy of the D3CERoS. I tried to "upgrade" my digital deluxe version to the Collectors Edition but this has failed because the Digital Deluxe and Collectors Edition are considered the same thing in the Blizzard library. If I had the base version of Reaper of Souls then I would have been able to successfully upgrade to the Collectors Edition but because a version of the CE of RoS was already on my account I am unable to actually tell Blizzard accounts that I have a physical copy beyond a picture on Twitter.
I have two copies of the DFF closed beta, however my account (and everybody else's accounts) is only able to redeem one of those codes. The codes are inactive so if you try to redeem one right now you will get an error saying that either the code is invalid or has already been redeemed. Inactive codes will bring this up and Friday at 9PM PDT we should be able to redeem the codes and download the beta.
TLDR, try redeeming your code after 9PM PDT on Friday because codes are inactive right now and you can only have one copy of any game tied to a PSN account so I gave my extra to a friend.