You may do that but the line will require a vent. The vent has to go through the roof or, tie into an existing vent on the floor above. A vent will not have waste water flowing in it. There are also specific requirements as to how the vent ties in relating to distance above the flood rim of the fixtures served by that vent.
The standpipe length should be 18 - 30" in length under most codes and the pipe and trap used should be 2" pipe.
Now how that adds up in height and whether or not your washer can drain that high I don't know. If it doesn't you will have to use a laundry tray pump like a Liberty 405.