  This paper is concerned with the investigation of the massless regime of an
integrable spin chain based on the quantum group deformation of the $OSp(3|2)$
superalgebra. The finite-size properties of the eigenspectra are computed by
solving the respective Bethe ansatz equations for large system sizes allowing
us to uncover the low-lying critical exponents. We present evidences that
critical exponents appear to be built in terms of composites of anomalous
dimensions of two Coulomb gases with distinct radii and the exponents
associated to $Z(2)$ degrees of freedom. This view is supported by the fact
that the $S=1$ XXZ integrable chain spectrum is present in some of the sectors
of our superspin chain at a particular value of the deformation parameter. We
find that the fine structure of finite-size effects is very rich for a typical
anisotropic spin chain. In fact, we argue on the existence of a family of
states with the same conformal dimension whose lattice degeneracies are
apparently lifted by logarithmic corrections. On the other hand we also report
on states of the spectrum whose finite-size corrections seem to be governed by
a power law behaviour. We finally observe that under toroidal boundary
conditions the ground state dependence on the twist angle has two distinct
analytical structures.
