  We conduct systematic calculations of the S-wave fully strange systems with
``normal" $\left(J^{P C}=0^{++}, 1^{+-}, 2^{++}\right)$ and ``exotic"
$\left(J^{P C}=0^{+-}, 1^{++}, 2^{+-}\right)$ C-parities, which are the strange
analogue of the fully charmed tetraquark state $X(6900)$. Within a constituent
quark potential model, we employ the Gaussian expansion method to solve the
four-body Schr\"odinger equation and the complex scaling method to identify
resonant states. We obtain a series of resonant states and zero-width states in
the mass range of 2.7 to 3.3 GeV, with their widths ranging from less than 1
MeV to about 50 MeV. Their rms radii strongly indicate that they are compact
tetraquark states. Among these states, the $T_{4s,2^{++}}(2714)$ may be the
most likely one to be observed experimentally. We urge the experimental
exploration of the $2^{++}$ $s s \bar{s} \bar{s}$ state around 2.7 GeV in the
$\phi\phi$ channel. Since the lowest S-wave $s s \bar{s} \bar{s}$ state is
around 2.7 GeV, the compact P-wave $s s \bar{s} \bar{s}$ states are expected to
be heavier. Hence, $\phi(2170)$ and $X(2370)$ are unlikely to be compact
tetraquark states.
