  We provide a numerical investigation of two families of subsystem quantum
codes that are related to hypergraph product codes by gauge-fixing. The first
family consists of the Bravyi-Bacon-Shor (BBS) codes which have optimal code
parameters for subsystem quantum codes local in 2-dimensions. The second family
consists of the constant rate "generalized Shor" codes of Bacon and Cassicino
\cite{bacon2006quantum}, which we re-brand as subsystem hypergraph product
(SHP) codes. We show that any hypergraph product code can be obtained by
entangling the gauge qubits of two SHP codes. To evaluate the performance of
these codes, we simulate both small and large examples. For circuit noise, a
$[[21,4,3]]$ BBS code and a $[[49,16,3]]$ SHP code have pseudthresholds of
$2\times10^{-3}$ and $8\times10^{-4}$, respectively. Simulations for
phenomenological noise show that large BBS and SHP codes start to outperform
surface codes with similar encoding rate at physical error rates $1\times
10^{-6}$ and $4\times10^{-4}$, respectively.
