  In this paper we investigate codes over finite commutative rings R, whose
generator matrices are built from \$\alpha\$-circulant matrices. For a
non-trivial ideal I<R we give a method to lift such codes over R/I to codes
over R, such that some isomorphic copies are avoided.
  For the case where I is the minimal ideal of a finite chain ring we refine
this lifting method: We impose the additional restriction that lifting
preserves self-duality. It will be shown that this can be achieved by solving a
linear system of equations over a finite field.
  Finally we apply this technique to Z_4-linear double nega-circulant and
bordered circulant self-dual codes. We determine the best minimum Lee distance
of these codes up to length 64.
