  Continuous-variable cluster states allow for fault-tolerant measurement-based
quantum computing when used in tandem with the Gottesman-Kitaev-Preskill (GKP)
encoding of a qubit into a bosonic mode. For quad-rail-lattice macronode
cluster states, whose construction is defined by a fixed, low-depth beam
splitter network, we show that a Clifford gate and GKP error correction can be
simultaneously implemented in a single teleportation step. We give explicit
recipes to realize the Clifford generating set, and we calculate the logical
gate-error rates given finite squeezing in the cluster-state and GKP resources.
We find that logical error rates of $10^{-2}$-$10^{-3}$, compatible with the
thresholds of topological codes, can be achieved with squeezing of 11.9-13.7
dB. The protocol presented eliminates noise present in prior schemes and puts
the required squeezing for fault tolerance in the range of current
state-of-the-art optical experiments. Finally, we show how to produce
distillable GKP magic states directly within the cluster state.
