  We perform Monte Carlo simulations of a lattice gauge system with an action
which contains two parallel plaquettes. The action is defined as a product of
gauge group variables over two parallel plaquettes belonging to a given
three-dimensional cube. The peculiar property of this system is that it has
strong degeneracy of the vacuum state inherited from corresponding gonihedric
$Z_2$ gauge spin system. These vacuua are well separated and can not be
connected by a gauge transformation. We measure different observables in these
vacuua and compare their properties.
