  We extend the Kitaev model defined for the Pauli-matrices to the Clifford
algebra of $\Gamma$-matrices, taking the $4 \times 4$ representation as an
example. On a decorated square lattice, the ground state spontaneously breaks
time-reversal symmetry and exhibits a topological phase transition. The
topologically non-trivial phase carries gapless chiral edge modes along the
sample boundary. On the 3D diamond lattice, the ground states can exhibit
gapless 3D Dirac cone-like excitations and gapped topological insulating
states. Generalizations to even higher rank $\Gamma$-matrices are also
discussed.
