A clothes washer has a pump built into it, the manual for the washer should tell you how high it can pump. For example, the last one I bought says that the discharge from the washer has to be 30" to 96" above the bottom of the washer.
You'd still need vertical clearance for a standpipe and trap (and a vent for the trap, which could be an AAV), and so the washer would have to be able to pump to the top of the standpipe. It might work if your sewer line exits the basement at 4' AFF, not likely to work at 8' AFF, and a maybe at 6' AFF.
And this wouldn't help you for a laundry sink, for that you'll need a separate basin and pump.
Cheers, Wayne