  Spin chains with symmetry-protected edge modes are promising candidates to
realize intrinsically robust physical qubits that can be used for the storage
and processing of quantum information. In any experimental realization of such
physical systems, weak perturbations in the form of induced interactions and
disorder are unavoidable and can be detrimental to the stored information. At
the same time, the latter may in fact be beneficial; for instance by
deliberately inducing disorder which causes the system to localize. In this
work, we explore the potential of using an $XZX$ cluster Hamiltonian to encode
quantum information into the local edge modes and comprehensively investigate
the influence of both many-body interactions and disorder on their stability
over time, adding substance to the narrative that many-body localization may
stabilize quantum information. We recover the edge state at each time step,
allowing us to reconstruct the quantum channel that captures the locally
constrained out of equilibrium time evolution. With this representation in
hand, we analyze how well classical and quantum information are preserved over
time as a function of disorder and interactions. We find that the performance
of the edge qubits varies dramatically between disorder realizations. Whereas
some show a smooth decoherence over time, a sizeable fraction are rapidly
rendered unusable as memories. We also find that the stability of the classical
information -- a precursor for the usefulness of the chain as a quantum memory
-- depends strongly on the direction in which the bit is encoded. When
employing the chain as a genuine quantum memory, encoded qubits are most
faithfully recovered for low interaction and high disorder.
