.MPG to Plex

I have an .MPG file burned onto a Blu-Ray disc. It's an HD DVR recording that was copied from a Cable DVR. I'm trying to get this recording onto Plex. The .MPG file plays perfectly fine using software (VLC, etc.). But to get it on Plex, it needs to be an MP4 or an MKV. What can I use to convert it without losing any quality? MakeMKV will not work with the disc. It just scans it and then the big drive button is greyed out.

Thanks.