Good morning, @avanhornWelcome to the Canvas Community. Thank you for posting your question. I had to do a bit of searching here in the Community to find an answer for you, and I found the following past thread which I believe still applies today for current/legacy Quizzes: How can I assign a quiz to a group?. Does this help to answer your question?
I wish to do this, too. I looked for a work around, like creating a module that only opens for a particular group, but I don't see a way to do that, either. I'm not excited about adding 34 individual names. (I'm actually surveying a set of students who participated in a particular activity; I want their answers to be anonymous, which means I won't be able to throw out anyone who participates even if they aren't part of the intended group, so self-exclusion will not work.)