Where did you get your code? Unless you got it from coinbase it won't work. Did you follow all the steps written here (Just the Authy Part): https://support.coinbase.com/customer/en/portal/articles/1658338-how-do-i-set-up-2-factor-authentication-
To clarify, Did you already got an access to your account? and now you're just trying to set up your 2fa using an app? Because if it's not, there's no way that you can use any app as you haven't activated any based from your previous post.
For now, Only their support can help you. Now that you mentioned it, How did it go? Have you received a reply? Did you tell them that you haven't activated any app for 2fa as welll as the part where sms codes from other services are working fine except from theirs?
From what I know, this doesn't apply to authy