Unfortunately, Z's and Higgs bosons are extremely unstable, so collecting a gas of same is a tall order.
Neutrinos are stable and are practically non-interacting, but they are also practically massless.
In practice, all the other particles we have measured carry some other kind of charge, be it electromagnetic, weak or strong, but nothing in principle prevents there from being another type (or even class) of particles that don't interact except gravitationally. The universe could be brimming with them, but there's no way to detect them in the laboratory, just because of the fact that they carry no Standard Model charges. The only way to detect them would be through gravitational means.
[Geek alert: If there are extra dimensions, the possibility exists that a high-energy electron-positron collider could produce massive Kaluza-Klein "tower" graviton states. These in turn would couple to the gravitation-only dark matter states. You wouldn't see those dark-matter-producing collisions directly, as the final-state dark matter particles would escape, undetected as usual, but you could see a faint impression of them through Bremsstrahlung radiation from the initial-state electron and positron. This would manifest itself as events with a single, hard gamma ray, the distribution of which would be peaked in the forward direction (along the beam axis).]
(I mean that affectionately!) Thank you for the information!
I sure hope there isn't a quiz on this next period.
;-)
I think we tend to get in trouble when we use one hypothetical particle to explain the existence of another hypothetical particle. I agree that the Higgs should exist, but for now it is purely hypothetical.