  We introduce a one-dimensional plaquette orbital model with a topology of a
ladder and alternating interactions between $x$ and $z$ pseudospin components
along both the ladder legs and on the rungs. We show that it is equivalent to
an effective spin model in a magnetic field, with spin dimers that replace
plaquettes and are coupled along the chain by three-spin interactions. Using
perturbative treatment and mean field approaches with dimer correlations we
study the ground state spin configuration and its defects in the lowest excited
states. By the exact diagonalization approach we find that the quantum effects
in the model are purely short-range and we get estimated values of the ground
state energy and the gap in the thermodynamic limit from the system sizes up to
$L=12$ dimers. Finally, we study a class of excited states with classical-like
defects accumulated in the central region of the chain to find that in this
region the quantum entanglement measured by the mutual information of
neighboring dimers is locally increased and coincides with disorder and
frustration. Such islands of entanglement in otherwise rather classical system
may be of interest in the context of quantum computing devices.
