Dishwasher drain length

onto my next step- bought a Bosch DW with a reccomended max drain length of 150", which is pretty good compared to some at 92". My DW space (an unfortunate legacy of the former owner's stupidity) is located across the kitchen aisle from teh sink. The drain line is a ruber hose stretched across the basement's joists.. total length including up to the air gap approaches 150inches. So - they say you need a 20" rise in the line- doesn't the rise to the air gap provide that? And, if so, can I trim the DW's factory installed drain line to the minimum needed to pull the DW out (36" approx.) and plug it right into the rubber hose drain line with proper clamps-- thus eliminating the factory set 20" rise attached to the side of the DW? Or, is an extra 24" of drain length really going to matter? Thank you.