As has been said in the Lodestone notice and elsewhere, those who purchased the PC version at the SE Store are not being sent their codes all at once. They're being sent sequentially. I don't know if they mean in the order that the pre-order was placed, by last name or what.

A friend got their code in their email about 6 hours ago. Mine showed up 45 minutes ago. They're definitely getting distributed as described.

Also as others have pointed out, the code cannot be entered into the Mogstation until the game's official release (July 2nd). Getting it now and trying to enter it will only result in an error message as stated in the Lodestone notice.

As long as you have registered your pre-order code already, you'll be able to play Dawntrail when the servers come online.