Quasi-polycyclic (QP for short) codes over a finite chain ring R are generalization of quasi-cyclic codes, and these can be viewed as an R[x]-submodule $${\mathcal {R}}_m^{\ell }$$ , where {R}}_m:= R[x]/\langle f\rangle $$ f is monic polynomial degree m R. If factors uniquely into coprime basic irreducibles, then their algebraic structure allow us to characterize the generator polynomials minim...