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