  Majorana zero modes (MZMs) are promising candidates for
topologically-protected quantum computing hardware, however their large-scale
use will likely require quantum error correction. Majorana surface codes (MSCs)
have been proposed to achieve this. However, many MSC properties remain
unexplored. We present a unified framework for MSC "twist defects"
$\unicode{x2013}$ anyon-like objects encoding quantum information. We show that
twist defects in MSCs can encode twice the amount of topologically protected
information as in qubit-based codes or other MSC encoding schemes. This is due
to twists encoding both logical qubits and "logical MZMs," with the latter
enhancing the protection microscopic MZMs can offer. We explain how to perform
universal computation with logical qubits and logical MZMs while potentially
using far fewer resources than in other MSC schemes. All Clifford gates can be
implemented on logical qubits by braiding twist defects. We introduce
lattice-surgery-based techniques for computing with logical MZMs and logical
qubits, achieving the effect of Clifford gates with zero time overhead. We also
show that logical MZMs may result in improved spatial overheads for
sufficiently low rates of quasi-particle poisoning. Finally, we introduce a
novel MSC analogue of transversal gates that achieves encoded Clifford gates in
small codes by braiding microscopic MZMs. MSC twist defects thus open new paths
towards fault-tolerant quantum computation.
