CalyxOS Emulator images are built in largely the same way as the OS, just with a different target name.

Assuming that you have setup a build envrionment or already built CalyxOS once as described in Building CalyxOS.

For the emulator, the steps are:

cd ~/calyxos/android14
source build/envsetup.sh
breakfast sdk_phone_x86_64 # x86 for the 32-bit image.
m

You can now run emulator to directly launch the built image.