I'm not sure what the smallest case would be, but even though a case may say it can take a 360 radiator, it doesn't mean it can accommodate the 360 Phoenix.
The reason being, is that the reservoir & the pump unit, add an additional 55mm to the length of the radiator, so making the overall length 415mm.
I have mine in a Thermaltake Core X71, but this is a pretty large case.
The depth of this case is approx 500mm, and there is hardly any room left, so case wise, I don't think you should be looking at any case, less than 500mm in depth.