A couple of ideas. If you happen to be a Lightroom user, then I believe you could do this with the Lightroom Print module - you'd set it up as you want, with the size, settings etc, then export it as a file rather than actually printing it. I've done this with smaller sets of images (e.g. for a triptych), but I don't see any reason you couldn't do it with a large set like this, so long as you first put all the images you want to use into a single Lightroom Collection.
Also, I've made image collages as slides in PowerPoint, using as many as 20 or more images on a single slide, with overlaid images, angled images etc. I expect any slide you produce in PPT could then be exported as a jpg to use in some other program (though I haven't actually tried that). I've only done this as part of a PPT slide show, so I can't be sure how it would work for other purposes, but it should be experiment, using just a few images to start with. One thing I've noticed is that PPT creates very large files, so you'd probably want to be sure you're working from the smallest versions of the images that you can get away with using, before you begin.