When you purchase an in-game item/emote/gear etc for one of your characters, you won't get a code but it will be sent to your character by the Moogle Mail, so it's best to log in to the game to see if you have received anything.

If the item isn't received after a period of time but the payment was taken (and confirmed by the SE auto emails), then it would be best to contact them via Support and have them investigate.