  It is known that for the Heisenberg XXZ spin-$\frac{1}{2}$ chain in the
critical regime, the scaling limit of the vacuum Bethe roots yields an infinite
set of numbers that coincide with the energy spectrum of the quantum mechanical
3D anharmonic oscillator. The discovery of this curious relation, among others,
gave rise to the approach referred to as the ODE/IQFT (or ODE/IM)
correspondence. Here we consider a multiparametric generalization of the
Heisenberg spin chain, which is associated with the inhomogeneous six-vertex
model. When quasi-periodic boundary conditions are imposed the lattice system
may be explored within the Bethe Ansatz technique. We argue that for the
critical spin chain, with a properly formulated scaling limit, the scaled Bethe
roots for the ground state are described by second order differential
equations, which are multi-parametric generalizations of the Schr\"{o}dinger
equation for the anharmonic oscillator.
