The HTTP response code is just a number. It will be in the range 100 to 599 as given in the official IANA list. If you use LWP::UserAgent you can retrieve this number with the code method. If you should need to set the code (and I don't see why you should from what you've said so far) set it just to one of these integers and not to a message.
I am using Win32::NetAdmin to authrize my user with the user login from env variable. How do I bypass this with the UserAgent module?
I'm entirely unfamiliar with that module, and indeed with every module under Win32::* - you are on your own there. If it uses HTTP Basic Auth or if you supplant it with HTTP Basic Auth, then you could use the credentials method of LWP::UserAgent to authenticate.