That appears to be the same GeForce 4 MX440 I had years ago, down to the color, form factor, heatsink, outputs, exact capacitor layout, it all looks identical. Specifically, mine was a "GeForce4 MX440 w/AGP8x" at least as identified by drivers, and had 64 MB.
I never did know what brand it was. It came from some brand-less White box baby-AT socket 370 PC that was in a school. Trying to look it up back then, I never found anything definitive (I recall finding clues it might be either AOpen or PNY, but nothing concrete outside some online listings with a matching picture supposedly tagging it as either brand), and this thread isn't helping since those same things nowadays suggest it's Palit? But there's something I'm noticing...
The image in the first post has PMI (or DMI, whatever it is) branded memory. one of the links shows Hynix memory, and yet another link shows yet a third type of memory, yet the cards appear identical outside of this. I don't member what memory mine had, either (I want to say it was the same one pictured in the first post but I'm not certain). Whatever brand it was, did they make multiple of them with different memory? or did multiple brands use the same card and choose different memory? Seems to be a small mystery.
What I can tell you is this, at least if that is the same one I had. I recall that the memory used runs at a slower speed than the usual specs for the GeForce 4 MX440 with AGP8x state (should be 250 MHz/500 Mhz DDR, or at least 200 MHz/400 MHz DDR for the non-AGP8x version). Both links support this, so it seems regardless of what memory it has, it's slower than it should be. I found this out while I was learning to overclock, because the core of 275 MHz went to 300 MHz+, but the memory had absolutely no headroom (or very little) even though it was already below the spec I recall Nvidia listed it should be running at. I recall being disappointed but it explained why my card felt slower than results I found online. I think it was indeed as low as 150 MHz (300 MHz DDR), which matches what two earlier links show (one lists 300 MHz for memory speed, and another shows a GPU-Z screen showing 150 MHz).
In other words, beware as it's liable to be gimped below standard specs (and the MX440 was slow to begin with), regardless of bus width. I do believe it was 64-bit anyway.