  We build on recent work by B. Brown (Sci. Adv. 6, eaay4929 (2020)) to develop
and simulate an explicit recipe for a just-in-time decoding scheme in three 3D
surface codes, which can be used to implement a transversal (non-Clifford)
$\overline{CCZ}$ between three 2D surface codes in time linear in the code
distance. We present a fully detailed set of bounded-height lattice slices
through the 3D codes which retain the code distance and measurement-error
detecting properties of the full 3D code and admit a dimension-jumping process
which expands from/collapses to 2D surface codes supported on the boundaries of
each slice. At each timestep of the procedure the slices agree on a common set
of overlapping qubits on which $CCZ$ should be applied. We use these slices to
simulate the performance of a simple JIT decoder against stochastic $X$ and
measurement errors and find evidence for a threshold $p_c \sim 0.1\%$ in all
three codes. We expect that this threshold could be improved by optimisation of
the decoder.
