I'm going to assume you live in a rural area - which seems like the only place that would dischage a washing machine in such a manner. I'm also assuming you have a septic system, and the washer is not part of the septic system, because it would damage the naturally-occurring breakdown of matter.
Assuming all this is the case, I'd recommend putting in a gray water tank. Gray water is basically like a drywell. The gray - or used - water is held briefly in the tank before being discharged to an irrigation or treatment system. If an irrigation system, it discharges slowly back to the earth, generally on the opposite side of the house from the septic system. You never want to discharge to a grade like the one you described. The water in your pipes could easily freeze, which could result in clogging.