  The subject matter of this work is a 1D quantum spin - $\frac{1}{2}$ chain
associated with the inhomogeneous six-vertex model possessing an additional
${\cal Z}_r$ symmetry. The model is studied in a certain parametric domain,
where it is critical. Within the ODE/IQFT approach, a class of ordinary
differential equations and a quantization condition are proposed which describe
the scaling limit of the system. Some remarkable features of the CFT underlying
the critical behaviour are observed. Among them is an infinite degeneracy of
the conformal primary states and the presence of a continuous component in the
spectrum in the case of even $r$.
