  We present a scheme for universal topological quantum computation based on
Clifford complete braiding and fusion of symmetry defects in the 3-Fermion
anyon theory, supplemented with magic state injection. We formulate a
fault-tolerant measurement-based realisation of this computational scheme on
the lattice using ground states of the Walker--Wang model for the 3-Fermion
anyon theory with symmetry defects. The Walker--Wang measurement-based
topological quantum computation paradigm that we introduce provides a general
construction of computational resource states with thermally stable
symmetry-protected topological order. We also demonstrate how symmetry defects
of the 3-Fermion anyon theory can be realized in a 2D subsystem code due to
Bomb\'{i}n -- making contact with an alternative implementation of the
3-Fermion defect computation scheme via code deformations.
