  We calculate the mass spectrum of the $S$-wave fully-charmed tetraquark
resonant states $cc\bar c\bar c $ in the nonrelativistic quark model, which
successfully describes the charmonium spectrum. The four-body system is solved
with the Gaussian expansion method. The complex scaling technique is used to
identify the genuine resonances. With the nonrelativistic quark model, our
results show the existence of two $cc\bar c\bar c$ resonances in each of the
$J^{PC}=$ $0^{++}$, $1^{+-}$ and $2^{++}$ sectors, respectively. In the
$S$-wave sector, no resonance is found at the energy region of the $X(6200)$
and $X(6600)$ states. The lower $0^{++}$ and $2^{++}$ resonances are located
around $100$ MeV higher than the $X(6900)$ state observed in experiments but
have the decay widths consistent with the experiment. The higher $0^{++}$ and
$2^{++}$ resonances are found at around $7.2$ GeV with the widths of $60.6$ MeV
and $91.2$ MeV, respectively, and they may be good candidates for the $X(7200)$
state.
