  The framework of the so-called 3-3-1LHN model may accommodate two different,
but viable, scenarios of dark matter: one involving a heavy Dirac neutrino ,
$N_1$, or another having a scalar, $\phi$, as dark matter candidate. In both
cases the dark matter phenomenology, relic abundance and scattering cross
section off of nuclei, is controlled by exchange of $Z^{\prime}$. We then
investigate the impact on the parameter space $(M_{Z^{\prime}}\,,\,M_{(N_1\,,\,
\phi)})$ due to the recent Pandax-4T experimental result in both scenarios.
First, the Pandax-4T experiment excludes scenarios with dark matter mass below
$1.9$ TeV. Concerning $Z^{\prime}$, we find the lower bound $M_{Z^{\prime}}>
4.1$ TeV for the case when $N_1$ as the dark matter and $ M_{Z^{\prime}}>5.7$
TeV for the other case. This implies that the 3-3-1 symmetry is spontaneously
broken above $10$ TeV scale. We also comment on the contributions to the relic
abundance of processes involving flavor changing neutral current mediated by
$Z^{\prime}$.
