Got stuck with "You have exceeded your emergency code limit. Please contact your system administrator" on your synology?
Me too.. ..my mobile phone wend dead taking the Google Authenticator app with it and my trusty Synology DS411+II don't wont let me to log in without 2-auth.
This blogpost suggested to add your own reset codes to google_authenticator file - it didn't work for me :(
Here is my solution - I renamed the file.
Login with your admin account via ssh.
and rename (remove) the google_authenticator file
mv google_authenticator google_authenticator_backup
and logged me with my account via web interface and got this shiny 2-auth configuration dialog.