Robert,
25 11 1 221 202 @ around $30. This part is called the shift console.
It will be necessary to remove the so called bitch clip (#3 in your pic) to get the shift console out. It's quite difficult, but not impossible, to undo without lowering the back half of the transmission. Use a small flat head screwdriver, leveraged against the side (there's a metal tab on the side of the clip that holds it into place -- lifting straight up on the clip will bend or break that tab) to pop the clip up and out.
Now that the console is broken, you'll also want to replace the bushing, part number 25 11 1 222 039 (#2 in the pic), at around $20. Because the console broke, the rear bushing (#4) may be damaged -- if it is, the shifter height will lessen in the car and shifting will be sloppy. #4 is #25 11 1 220 707 (around $20).
You might consider buying the console used, but the bushings should be purchased new. I know they're a bit of money, especially considering the ~ $30 cost of the Z3 shifter, but you'll be glad that they were replaced when everything was apart (versus later, when everything's back together). Use a bit of Molybdenum grease on the contact points when putting it all back together. Good luck!