  We construct a gauge theory based in the supergroup $G=SU(2,2|2)$ that
generalizes MacDowell-Mansouri supergravity. This is done introducing an
extended notion of Hodge operator in the form of an outer automorphism of
$su(2,2|2)$-valued 2-form tensors. The model closely resembles a Yang-Mills
theory -- including the action principle, equations of motion and gauge
transformations -- which avoids the use of the otherwise complicated component
formalism. The theory enjoys $H=SO(3,1)\times \mathbb{R} \times U(1)\times
SU(2)$ off-shell symmetry whilst the broken symmetries $G/H$, translation-type
symmetries and supersymmetry, can be recovered on surface of integrability
conditions of the equations of motion, for which it suffices the
Rarita-Schwinger equation and torsion-like constraints to hold. Using the
\textit{matter ansatz} -- projecting the $1 \otimes 1/2$ reducible
representation into the spin-$1/2$ irreducible sector -- we obtain (chiral)
fermion models with gauge and gravity interactions.
