  We report a detailed CO(1-0) survey of a galaxy protocluster field at
$z=2.16$, based on 475 hours of observations with the Australia Telescope
Compact Array. We constructed a large mosaic of 13 individual pointings,
covering an area of 21 arcmin$^2$ and $\pm6500$ km/s range in velocity. We
obtain a robust sample of 46 CO(1-0) detections spanning $z=2.09-2.22$,
constituting the largest sample of molecular gas measurements in protoclusters
to date. The CO emitters show an overdensity at $z=2.12-2.21$, suggesting a
galaxy super-protocluster or a protocluster connected to large-scale filaments
with ~120 cMpc size. We find that 90% CO emitters have distances $>0'.5-4'$ to
the center galaxy, indicating that small area surveys would miss the majority
of gas reservoirs in similar structures. Half of the CO emitters have
velocities larger than escape velocities, which appears gravitationally unbound
to the cluster core. These unbound sources are barely found within the
$R_{200}$ radius around the center, which is consistent with a picture in which
the cluster core is collapsed while outer regions are still in formation.
Compared to other protoclusters, this structure contains relatively more CO
emitters with relatively narrow line width and high luminosity, indicating
galaxy mergers. We use these CO emitters to place the first constraint on the
CO luminosity function and molecular gas density in an overdense environment.
The amplitude of the CO luminosity function is 1.6$\pm$0.5 orders of magnitudes
higher than observed for field galaxy samples at $z\sim2$, and one order of
magnitude higher than predictions for galaxy protoclusters from semi-analytical
SHARK models. We derive a high molecular gas density of $0.6-1.3\times10^{9}$
$M_\odot$ cMpc$^{-3}$ for this structure, consistent with predictions for cold
gas density of massive structures from hydro-dynamical DIANOGA simulations.
