The pump on a washing machiene is designed to pump volume not height, but could you not find where your main drain is as it may be lower than or very close to the depth of your basement.
If it isnt then i suggest you dont put the m/c in the basement. I say this not through sarcasm but praticality, to have a separate pump you would need to have a pump chamber, automatic pump. You could use a sump pump with automatic float switch, but these will only pump out water to within a depth of 2cm so that would mean your sump would always have some water in it which is liable to stagnate and smell (especially if the m/c is not used for some time)
In theory you could connect the output of the m/c to a amphibious pump, but as most of these are designed for ponds it may soon get clogged up with lint, not to mention the cost of one, then there is the problem of starting it, yes you could just use a on / off switch but if you forget to turn it off, bye bye pump as if left running dry for some time it will burn out