Install OS X recovery mode. Can't log in
The version of the operating system of the recovery partition is probably lower than 10.11.0.

According to Apple you have to append the auth code to the password then:


  What if I use two-factor authentication on a device running older software?
  If you use two-factor authentication with devices running older OS versions, you might be asked to add your six-digit verification code to the end of your password when signing in. Get your verification code from a trusted device running iOS 9 and later or OS X El Capitan and later, or have it sent to your trusted phone number. Then type your password followed by the six-digit verification code directly into the password field.