There are a couple of alternatives to your problem that come to mind, although we are reluctant to suggest one over the other for a lack of more specific information. What you might want to do is review both of these suggestions with a qualified plumbing contractor who can assist you in making a decision on which alternative best suits your situation.

The first solution involves connecting the new waste line from the washing machine into the existing sanitary sewer system at a point which is lower than and in reasonably close proximity to the garage. The fact that the house is higher than the garage doesn't exclude the possibility that the sewer that supplies your home is, at some point (between the house and the street or adjacent property), lower than the garage. If this happens to be the case, you're as good as washing cloths in the garage as we write these very words.

In the event that our first suggestion will not work in your case then you should consider having a holding tank installed that your washer can discharge into. The holding tank accepts the waste water and upon reaching a certain level will automatically pump it up to a plane where the water can be discharged into the sanitary sewer system. Special back-flow devices must also be installed to prohibit the waste water from backing up into the holding tank. This system will also work for those of you who may be considering a shower in your basement!