  Construction $C^\star$ was recently introduced as a generalization of the
multilevel Construction C (or Forney's code-formula), such that the coded
levels may be dependent. Both constructions do not produce a lattice in
general, hence the central idea of this paper is to present a 3-level lattice
Construction $C^\star$ scheme that admits an efficient nearest-neighborhood
decoding. In order to achieve this objective, we choose coupled codes for
levels 1 and 3, and set the second level code C2 as an independent linear
binary self-dual code, which is known to have a rich mathematical structure
among families of linear codes. Our main result states a necessary and
sufficient condition for this construction to generate a lattice. We then
present examples of efficient lattices and also non-lattice constellations with
good packing properties.
