How do you put a washing machine in a basement? You could plumb it to the grinder toilet you already have but that puts extra running time on that pump. How about a sump pump? Let the washing machine drain it's gray water into a 55gallon drum with a sump pump in it. Or you can buy a basin with a pump. Now you can pump that gray water outside or into your existing sewage line. I would make sure to use a water trap if connecting to the sewage line in your basement ceiling.