At least with my Z3100, you can't directly set the head height (or platen gap). Instead it's specified by the paper preset you choose. HP has published a number of PDF's that spell out the recommended presets for various paper types, and the head height that is specified by each preset. There are only two choices; low and high. Print a thick cotton rag paper with a low head height, and you'll get head strikes.
The HP Z printers don't use any vacuum system to keep papers flat, depending instead on all those little wheels and rollers. Consequently some papers can cockle (or ripple) under heavy inkloads, leading to head strikes even with the high setting. That's what made HP's own 'baryte satin' photo paper unusable on the Z3100 in my experience.