Answer:
The blizzard authenticator code is a code provided by either a small hardware device from blizzard or mobile phone app and is required only if you have attached the authenticator to your account.
If you did NOT attach one to your account, then that means you have been hacked. Call blizzard immediately to have it removed. And before you choose a different password, make sure you clean your computer out really good as you definitely have some type of key-logger on your system.