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:
dzvkheWelcome to the SmartX Fan Team! Now all of us collect free tokens. By the end of the year the launch of the mainnet is planned after which there should be a swap of erc-20 tokens to native tokens of the BlockDAG network. Listing on the exchange is due to take place this year. While there is no information on the exact timing of the listing. In the meantime follow the news and join all giveaways