Relocating washing machine in basement

Moving my washing machine about 20 feet from current location (and 20 feet from main vent stack) so installing new p-trap, drain, and vent. P-trap and drain will be 2 inch; vent 1.5 inch.

I understand (based on 248CMR 10.16(12)(a)) that the vent needs to be within 6 feet of the trap, but does the vent need to be vertical all the way from the drain connection up through the roof? I'd prefer to offset the vent about 3 feet so it can run up through the inside corner of a coat closet on the first floor. The vertical section of the vent will still be within 6 feet of the P-trap. I have no way of positioning the P-trap and drain so the vent could go straight up through the preferred position in the closet.



Bad sketch of the situation attached!

 

Thanks for the reply - I think that can work.

Rather than the vent going up through roof in the attic above closet, can I go back 20 feet horizontally in the attic and tie into the main 3-inch vent stack?

 

Also, is it just the first section of vertical vent that has to be within the specified distance (6 ft in this case) from the P-trap before the horizonal offset section. In the example posted could the horizonal offset be to the right (blue line added) and then the continuation of the vent vertically be outside of the 6 ft specified distance?