Postgres has a extension called cube (https://www.postgresql.org/docs/9.6/cube.html) that can be used for up to 150 dimensions (which is a compile-time limit, you can have more if you compile Postgres yourself).

It's a pretty cool extension that does distance between points, intersections between n-dimensional cubes (hence the name), different distance metrics etc.

It'd be perfect for storing and searching through large amounts of n-dimensional embeddings, I'm guessing it's used for that already.