What's the strongest anchor for something heavy in double drywall?
I think this question warrants an answer with a healthy dose of caution:

Shelves for supporting a lot of weight should not be supported via drywall! Structural shelves need to be supported by proper framing...namely the studs within the wall. 

Given that there is a party wall, if this is a condo, the walls may very well be made using steel studs. Depending on the gauge of steel studs, they may be able to support a wall shelf system, but maybe not.

The other issue is that you shouldn't put holes in party walls without permission. A party wall is shared property and your lease or title likely has some conditions pertaining what can and can not be done to a party wall on your own. 

The two main reasons to be cautious is fire codes (the double sheetrock is to meet shared wall fire codes and putting a hole in it defeats that) and sound (ideally, the party wall is fairly soundproof between units...creating holes, as well as attaching items to framing will allow more sound transmittance). 

Suggestion:

Consider a floor-based shelving system. Many of the wall shelving systems on the market also have the option to convert them to freestanding. Ikea's system, for example, can be installed with feet to make it freestanding: