Running Go on a JetBrains hosted Teamcity Windows build agent

I'm going to try to word this properly but if not then forgive me. 

We are trying to migrate from on-prem Teamcity install to the JetBrains hosted Teamcity. We have an executable that needs to be built using Go but on Windows. It needs to be a Windows executable. When we use the JetBrains hosted agents they default to the Linux one and only build Linux executables using Go.  When we force it to use the Windows agents it fails because the Windows agents do not have Go installed. Since on-prem we could install whatever we wanted this was not an issue. 

How do I build this executable using Go but on the Windows platform? My idea was to use a Docker Windows container and install Go on it and then run that on the build agent. (Not sure if this is possible). I am still learning about containerization so not sure if this is feasible. The whole point of this is to not run any new VMs anywhere and use the JetBrains hosted agents. Any other alternatives I should look at? The executable requires a specific Windows software so it cannot be run on Linux.