Apple has rejected the app and suggests two options : Volume purchase program and Enterprise program
If your app is in fact targeting both employees and people external to the company, then the Public App Store is your only choice anyway. All other options like VPP or the Apple Developer Enterprise Program do only allow you to distribute apps to employees. So your argumentation towards Apple would be that it needs to be the public store, because there is no other way to distribute that app to a potentially global audience.

However they might not like your authentication method "unique code", as Apple usually wants apps to have a signup method and a more sophisticated login, such as username and password.

Adding some external (publicly visible) content near the login might help to get the App approved as well.