I'd put in a sand pit for the pipe to empty into and let that spill out into your flower beds.
Our set up like this is only about 10 feet from the back of the house to the pit (I also have a reed bed with fungi in the line up) from these it spills into our
root vegetable garden space.
Our set up handles all sinks,
shower and laundry water. The system starts about 3 feet from the back wall of the house; gravel, sand, reed, moss and fungi, sand, garden beds is the order of flow through.
We found out this year that we might want to put our beans into that area, some of the beets split from to much water this year. (record rains have created an over abundance of water this year)