Quackgrass and Plastic Mulch

I am looking for help with a difficult field.

This field is on a certified organic farm, and is poorly drained, limiting
the amount of preplant tillage that can be done.  There is quite a bit of
quackgrass in it.  Timely cultivation is also difficult due to the drainage

We are thinking about using plastic mulch, but are wondering if the
quackgrass will grow right through it.  Is there a minimum gauge of plastic
necessary to hold it back?

Thank you for your suggestions and experiences.

Rob and Pam Flory
Pam's Garden
Lambertville, NJ