Of course, I've used Michelin tires before, but not the primacy MXM4. Specs look like this particular tire is designed to provide a good ride, while handling and traction are secondary. This seems at odds with what a Z is all about, but that may be your priority. Michelin makes a good tire, but I think there may be some better options in an all-season tire.
Currently, my street Z rides on BFG G-Force Comp 2 A/S plus and it has proven to be a good option for driving in my home state of Colorado.