Ask HN: What's the best way to up-scale an image?

I have a few 256 px x 256 px images. I need to enlarge them as much as possible while minimizing distortion. I'd like to turn them into a wall poster.

Do you have any advise on what to do to get the best result?

I've tried to directly enlarge them with photoshop but the details gets lost and they look terrible.

Is there a better way to do it?