I went on my steam profile (note these are all PC games, but some are on console) and looked at all the games I finished in under 20 hours at least once and enjoyed so I'll just list them here. It's in descending order from most (20.1 hours) to least (68 minutes):
I put a star next to the ones I'd recommend in a heartbeat even without the 20 hour limit.
- Mirror's Edge ★
- The Stanley Parable ★ (although may take you at least 20 to find all endings / easter eggs / secrets)
- Deus Ex: Mankind Divided ★ (due to the fact that it's the middle game in an incomplete trilogy, also recommend Deus Ex: Human Revolution but that's more than 20)
- Hotline Miami ★
- Little Inferno
- Tom Clancy's Splinter Cell
- Dishonored ★
- Myst
- DOOM (2016) ★
- Wolfenstein: The New Order ★
- Portals 1 & 2 ★
- Return of the Obra Dinn ★ (beat twice in 9 hours)
- Kentucky Route Zero ★
- The Henry Stickmin Collection ★
- FAR: Lone Sails
- Titanfall 2
- DUSK ★
- COD: Modern Warfare 2
- Ghostrunner (didn't like this but it seemed most people who weren't me did so i'm putting it here)
- Thomas Was Alone
- Jazzpunk: Director's Cut ★
- Gunpoint ★
- Orwell
- Firewatch
- Superliminal ★
- Observer_ ★
- SUPERHOT ★
- The Beginner's Guide
- BattleBlock Theater
- INSIDE ★
- EDGE
- Quadrilateral Cowboy
- Journey ★
edit: saw u said "story heavy" so i removed some of the arcadey ones. Some of these aren't exactly "story heavy" depending on ur definition but they at least have a story