  We analyze the properties of a 2D topological code derived by concatenating
the [[4, 2, 2]] code with the toric/surface code, or alternatively by removing
check operators from the 2D square-octagon or 4.8.8 color code. We show that
the resulting code has a circuit-based noise threshold of $\sim 0.41\%$
(compared to $\sim 0.6\%$ for the toric code in a similar scenario), which is
higher than any known 2D color code. We believe that the construction may be of
interest for hardware in which one wants to use both long-range two-qubit gates
as well as short-range gates between small clusters of qubits.
