Are you sure that code is what you need to enter? It sounds like the request identifier.
Does it look like this?
If so, and you don’t have the option to open the Authenticator on the Battle.net App, it might be trying to connect to the old version of the Authenticator App. That was retired on the 5th of this month.
If you have SMS set up, you may be able to use the Self-Help option to remove the Authenticator.