  The S=3/2 Kitaev honeycomb model (KHM) is a quantum spin liquid (QSL) state
coupled to a static Z$_2$ gauge field. Employing an SO(6) Majorana
representation of spin 3/2's, we find an exact representation of the conserved
plaquette fluxes in terms of static Z$_2$ gauge fields akin to the S=1/2 KHM
which enables us to treat the remaining interacting matter fermion sector in a
parton mean-field theory. We uncover a ground-state phase diagram consisting of
gapped and gapless QSLs. Our parton description is in quantitative agreement
with numerical simulations, and is furthermore corroborated by the addition of
a $[001]$ single ion anisotropy (SIA) which continuously connects the gapless
Dirac QSL of our model with that of the S=1/2 KHM. In the presence of a weak
$[111]$ SIA, we discuss an emergent chiral QSL within a perturbation theory.
