Now some genius wrote a DSM package to help you with this hassle.
The package is found here: https://github.com/oznu/homebridge-syno-spk
Download the SPK file and install this on your Synology nas in the package manager with manual install.
Also install the Docker application from the package manager (search for Docker).
After the installation you can find the Homebridge icon in you DSM apps and this opens the configuration page of homebridge.
Here you can install the needed plugins and edit the config file.
After editing reboot the package and watch the log if everything is running smoothly, if not fix the errors in the config file and restart again.