I have a basement washing machine and when it discharges the water it flows back out of the drain which is the same height as the washing machine. All the other drains in the house seem to be fine except for this one

Likely, the drain line or the trap for the washer is clogged with lint, detergent, and fabric softener.

You'll need to clean out the drain line. If it is just draining slowly, you might try pouring some VERY VERY hot water down - be careful, this can be tricky to accomplish in most cases.

Fabric softeners tend to be "gooey" and accumulate, with the lint over time. This might loosen up the "goo" and flush it on down. Follow up, once you've got it moving again with a washer full of HOT water.

If it is plugged totally, you'll need to snake out the line 1st, then follow with the hot water treatment. Use a long enough snake to get well past the trap and on down the drain line back to the larger main sewer line.

Let us know if you need more help.