There was some discussion on reddit about this last year, and the consensus is that the zip codes were not published and likely wouldn't be.

One person worked the paper's methodology backwards and came up with a list of potential candidate cities: https://old.reddit.com/r/todayilearned/comments/i3hb3c/til_t...

Kind of shocked me that I'm nowhere near any of those, as I feel like one of those harbingers (and I feel no desire to move to any of those places).