As a personal project I decided to configure my own Matrix server running on matrix.smoopy.org using the open source software Synapse.
You will notice that matrix.smoopy.org redirects you to chat.smooopy.org, this is because I am also hosting my own Element instance. So both the client and server are hosted on smoopy.org. However, you don't have to use the client I'm hosting, its just there for convienence. In fact you can use the Element client on element.io to connect to my Matrix server simply by changing the home server address to point to matrix.smoopy.org. Alternatively you can use one of the many other clients to connect as well.
Currently my server is set to public. So feel free to join and say hello!
I will make a follow-up post describing how to set up and configure your own Matrix and Element instance using docker-compose.