D&D. If 5e doesn't work, playing 1 or 2e...or even Basic/BECM for that matter would do the trick.
I don't really think "gritty" is a system reliant thing.
Are the characters in legitimate danger they may or truly may not be able to handle? Is magic somewhat restricted and/or rare? Is healing difficult (and/or, again, healing magic very difficult to come by) and/or lengthy?
Gritty as opposed to high fantasy, which D&D very clearly is.