Great question @BKapocias!

Yes, you can set an access code for a New Quiz.  The settings for New Quizzes are just in a different place. Once you are in the Build window where you can add questions, look a the tabs at the top of the page.  Switch to the Settings tab and one of the options should be Require a student access code.

Here is a Canvas guide that discusses this setting and other New Quizzes settings: How do I manage settings for a quiz in New Quizzes? 

Hope this helps!