As far as I know, registration for the game itself is not yet open. That's why you're not yet able to put a support ticket in for this. The only codes available to input now are the PS Store promotional codes being sent out for the open beta client. On August 20th, we'll be able to register pre-order codes to our accounts for the in-game items. I assume what you're trying to do won't be available until the 27th. The game is not out yet. There's no need to register it to your account yet.
I thought that might be the issue. What bothers me about it, though. Is that I was able to register my game on my account already. http://prntscr.com/1l9d7d
Either I made a boo-boo, something's wrong with her code, or the website is just being strange.
When you pre-order the game from the SE store, they send you an email with a serial code in it. I registered that serial code on the website in my link, and it worked right away. Hers is just saying "invalid code". If this isn't anything but just a weird coincidence, then that's fine. I just want to make sure we're both able to play the game during Early Access and on release day.
FFXIV: Raxion Gunsoul - Brynhildr - 50PLD 50SMN 50SCH 50DRG
WoW: Raxion - Greymane- 90 Druid
FFXI: Nion - Asura - 99 BLU, PUP, SMN, DRG, PLD 50+ DNC, NIN, MNK, THF, WHM, SAM, WAR