Pixy currently uses Keil MDK-ARM version 5.
Keil is basically free for university users, but requires a paid license normally.
To compile the firmware with Keil, you just point the IDE to the “workspace.uvmpw” workspace file in ~src/device/main_m4. It will open a workspace with 4 different projects: main_m4, main_m0, libpixy_m0, libpixy_m4. Compile the 4 projects in this order: libpixy_m4, libpixy_m0, main_m0, then finally the main_m4 project. The main_m4 project will create a firmware.hex output file that you can then upload into Pixy using firmware upload mode.
If you'd like to modify or create your own firmware using a (practically) free tool from NXP (LPCXpresso), which uses GCC, please join our firmware SDK group. LPCXpresso support for the Pixy2 firmware hasn't been added yet, but it should (hopefully!) be straightforward.