Vent for wall hung toilet with Geberit concealed tank

[Wuliao]

Hi, I am try to install wall hung toilet with Geberit concealed tank. It is horizontal drain in crawl space. The toilet requires 3 inch vertical drain inside 2x4 wall and I can not run vent within the same two 2x4 that hang the tank. Can I route the vent shown in picture? There is nothing upstream.
Thanks!

 

[Terry]

Wye off before the 90 and raise the grade on it.
You don't want to drop into a 3x2 santee where the waste will go both directions.

Is there a lav that can wet vent the toilet?