Dish washer drain hose routing
You want to make the run as high as possible early on and here's why.

If you mount it low, then the water comes off the pump with a lot of energy, runs along (losing energy) and then has to climb a hill. This means that you have a potential backwash situation and you have a LOT of water sitting in the drain line. I found this comment from Bosch to be helpful


  The high loop in the drain hose of your dishwasher is to keep water from settling in the hose if it were hanging down any lower or horizontally. This keeps the drain hose dried out and keeps any odors from backing up into the dishwasher.


So I would run the drain line high and then slope it down so can drain and stay empty and dry. The less water you have standing in the line, the better.