If it hasn't begun downloading yet:

Go to the PSN store
Navigate to your Library
Select FFXIV
Navigate to Add-On's
Select the download arrow. It should inform you if it begins downloading or has already been downloaded.

After this file installs (or has been installed), start the launcher to download the patch (if you haven't already).

They informed us that PSN is handling all of the codes thusfar for digital downloads. So we won't get separate ones to input.