Sound proof box

I have finally got my proxxon conversion fully up and running but and
the only problem with it is the noise. My house ajoins another and
there is no chance I can mill on an evening.

I'd like to make a sound proof box for it and have already made a
2.5" thick polystyrene cover for it that now just requires a "double
glazed" door. However after trying it last night with some foam
jammed in as a door it was anything but sound proof. Sitting the
mill on some foam did help a little but is not ideal.

Has anyone built such an enclosure? Would it be worth lining it with
egg box foam? Should it be clad with a hard material like MDF as
well? Is there a way of making a decent base for the mill that will
not turn my bench into a sound box?

Help

Graham