Unable to use discount codes when registering in admin area
As the error states, if you use the built-in fees section or a price set with a required price field option (of which you should always have at least one), you will not be able to submit the registration without selecting an option, even if it is a $0 option after applying a discount.

That said, no need to create a separate price set (especially when you are offering only one fee option) - all you need to do is select the $0 option after applying the discount code (or save yourself a click by making the fee option the default), then click the Save button - this will record the registration with a $0 contribution.

If you add a click and remove the "Record payment?" flag that is checkmarked by default when registering someone from the back-office, that will still result in a registration with a status of "Registered" but without the $0 contribution. 

Hope this helps,
Tamar