Moving washer and dryer to basement

I am getting ready to finish my basement and we want to move the washer and dryer down to the basement. My idea is to run the drain and vent inside a false wall. What I need to know is it ok to do this by code and should I use 2x4 or 2x6 for the wall. I have attached a crude drawing of my idea. The red line is the new drain and vent that would be inside the new wall. Also does anyone have suggestions on framing the wall to make it easier to go around the corner? I may also like to put in a utility sink if I can.

I wouldn't recommend drilling all the 2x4's in a wall for a length of 2" pipe, as there wouldn't be much left to the stud. You could run the pipes between the outside and a 2x4 wall, or you could build a 2x6 wall and drill it.

Most basement walls are not very flat, and building directly on it may lead to a wall that is wavy or not straight. You would also be risking moisture wicking into the wood from the outside walls. It would be forward-thinking to insulate the outside wall with 2" XPS foam board and build a stud wall to the inside of that. It would beat having to re-do it if you decided to finish the basement more in the future.

You haven't showed us anything that is against code, but you have not really showed us how you will install the pipe. You cannot connect the vent to a drain pipe in the basement. The vent must be within 6' of the trap at the washer and go up through the roof.

quote; You cannot connect the vent to a drain pipe in the basement. The vent must be within 6' of the trap at the washer and go up through the roof.

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Some places it is 4' from the trap, and just seeing two dots where the pipes are tells us NOTHING about how you intend to run the piping, ESPECIALLY if you also want to connect a sink to it.