You should have seen the message that Early Access has been applied to your account, once you entered that 20 digit code. Remember that rushing through a process is not helpful, when you are provided with all the information on the webpage.

I applied my early access code and the confirmation made was just the same as the webpage. So if you did everything correctly and logged into the right account when applying the code, then you have nothing to worry about and you will be able to play within the next 20 hours and 40 minutes

However with the error you received it probably applied the code to the account and due to high traffic the page tried to reload again and provided you with the information that the code has already been used.