You don't need to use 6-3-6-3 code is product registration as it is for Square-Enix Membership (social profile) site. The real game code is the 4-4-4 on PSN Redeem. If you want to have Square-Enix Membership, you can sign up, think of product registration to keep a shelf collection.

Square-Enix Account (one that use for FFXIV Service Account) is different from Square-Enix Membership.