If you are registering at the faucet for the first time don't push the button 'Join us'. You have to put your wallet in the account field and click login. The system will automatically recognize that your account has not yet been registered and on the next screen will prompt you to enter an invitation code. Everything is very simple!

Take into account that you must use your personal wallet such as MEW, Metamask, imToken etc. and your wallet must support erc-20 tokens
Thanks @dmvlzh, I finally managed to enter.

This probably confused me, it wasn't stated anywhere in the OP that the ETH address should be entered in the 'Please enter your account' field .
My invitation code:
dzvkhe