That was originally a Dynasound Organizer Cassette Tote Case that was readily available back during the production of TNG. They were primarily used as engineering kits or supply cases, except in the instance screen-capped above where one was used for the wall control panel.
I actually own two untouched Dynasound Organizers, with which I plan to do both Geordi's engineering kit as well as the wall control panel. Had a friend adept at LCARS graphics already do up the graphics for each control panel, just need to get a print shop to do them up for lighting.
These are actually very hard to find in any condition nowadays. I lucked out a couple years ago and came across an auction on eBay where one seller had two listed together, and I was the only one to bid on them.
EDIT: Interesting thing to note, they also widely used a narrower style of Dynasound Organizer Cassette Tote Case for some of the supply cases seen throughout TNG and even VOY.