  We investigate the quantum phases of monodispersed bosonic gases confined to
a triangular lattice and interacting via a class of soft-shoulder potentials.
The latter correspond to soft-core potentials with an additional hard-core
onsite interaction. Using exact quantum Monte Carlo simulations, we show that
the low temperature phases for weak and strong interactions following a
temperature quench are a homogeneous superfluid and a glass, respectively. The
latter is an insulating phase characterized by inhomogeneity in the density
distribution and structural disorder. Remarkably, we find that for intermediate
interaction strengths a {\it superglass} occurs in an extended region of the
phase diagram, where glassy behavior coexists with a sizable finite superfluid
fraction. This glass phase is obtained in the absence of geometrical
frustration or external disorder and is a result of the competition of quantum
fluctuations and cluster formation in the corresponding classical ground state.
For high enough temperature, the glass and superglass turn into a floating
stripe solid and a supersolid, respectively. Given the simplicity and
generality of the model, these phases should be directly relevant for
state-of-the-art experiments with Rydberg-dressed atoms in optical lattices.
