I have the same CPu but only one (which was expensive enough and Plex uses it well. Sometimes my clients say my Server is too slow but that’s just the client app being to stupid and not correctly pulling data from the server.
You can test if and how many cores Plex uses of your monster.
In Settings > Server > Transcoder set it to “Make my CPU hurt” and set “Background transcoding x264 preset” to “Very slow”.
On your Ubuntu install package htop (graphical top with usage bars, very handy). Open htop and configure it so you can see all cores and maybe the “All CPU avg” one too. Keep it running and start optimizing a movie in Plex.
Plex doesn’t use that much CPU but it should use all cores even a bit. If not enough resources are used you can fire up your clients and switch to a lower video quality so that these streams have to be transcoded too. This will help “making your CPU hurt”