No loop to hang dish washer drain hose higher
I think you have the right idea. It can't go behind the dishwasher - there is normally no space at all between the dishwasher and the wall.

Typically a dishwasher will be mounted next to a sink. The hose should be long enough that you can loop it up on the side or behind the sink so that it goes up to the bottom of the counter, or at least a few inches higher than the sink drain.

If the hose won't stay up by itself, screw a piece of metal or plastic strapping to the side or back of the sink cabinet near the top and loop it loosely around the hose to hold it up. Just don't loop it so tight that it crimps the hose.