What worked for me:

1. I did not get an email with the code. I logged into my Order Status on the SE Store and clicked "Receive Activation Code".

2. I logged in at redeem.finalfantasyxiv.com/na and entered my code. I then chose my platform, confirmed my platform and was given my Early Access Code.

3. I then logged into Mog Station and entered the Early Access code under the "Pre Order Early Access Code" tab. I copied and pasted it from the previous screen and it worked just fine.