Here's the Stomp rocket, already available on Thingiverse and Printable. It has received a few improvements to enable it to fly higher and faster.
This project was carried out in a fablab and I was not allowed to launch the rocket inside the building.

The piston was redesigned to push (or even hit) much harder, thus compressing even more air in the rocket. What's more, it is now possible to insert a gasket in the piston to seal it and prevent air loss during compression.

The launcher base has been improved to enable it to better conduct air into the rocket. The launcher is now removable and interchangable. This means it can be replaced in the event of breakage, but also with a resin-printed launcher that will be smoother and reduce friction even further.

Here are the parameters applied for each part:
Launcher base :
Material : PLA
Layer height: 0.2mm
Filling: 15%, gyroid
Number of perimeters: 2
Support: none
Nozzle temperature: 215°C
Bed temperature: 50°C

Launcher tube:
Material : PLA
Layer height: 0.15mm
Filling: 100%
Number of perimeters: 2
Support: none
Nozzle temperature: 215°C
Bed temperature: 50°C

Piston :
Material : PLA
Layer height: 0.2mm
Filling: 25%, gyroid
Number of perimeters: 4
Support: none
Nozzle temperature: 215°C
Plate temperature: 50°C

Rocket :
Material : ABS
Layer height: 0.15mm
Filling:
Number of perimeters: 2
Support: none
Nozzle temperature: 255°C
Plate temperature: 100°C
You can add a raft to improve the rocket's hold on the tray.