  With a substantial nuclear molecular gas reservoir and broad, high-velocity
CO molecular line wings previously interpreted as an outflow, NGC 1266 is a
rare SB$0$ galaxy. Previous analyses of interferometry, spectrally resolved
low-$J$ CO emission lines, and unresolved high-$J$ emission lines have
established basic properties of the molecular gas and the likely presence of an
AGN. Here, new spectrally resolved CO $J = 5 - 4$ to $J = 8 - 7$ lines from
{\it Herschel Space Observatory} HIFI observations are combined with
ground-based observations and high-$J$ {\it Herschel} SPIRE observations to
decompose the nuclear and putative outflow velocity components and to model the
molecular gas to quantify its properties. Details of the modeling and results
are described, with comparisons to previous results and exploration of the
implications for the gas excitation mechanisms. Among the findings, like for
other galaxies, the nuclear and putative outflow molecular gas are well
represented by components that are cool ($T_{nuclear} = 6^{+10}_{-2}$ K and
$T_{outflow} \sim 30$ K), comprising bulk of the mass (Log
$M_{nuclear}/M_{\odot} = 8.3^{+0.5}_{-0.4}$ and Log $M_{outflow}/M_{\odot} =
7.6^{+0.3}_{-0.3}$), and the minority of the luminosity (Log
$L_{nuclear}/L_{\odot} = 5.44^{+0.22}_{-0.18}$ and Log $L_{outflow}/L_{\odot}
\sim 6.5$) and warm ($T_{nuclear} = 74^{+130}_{-26}$ K and $T_{outflow} > 100$
K), comprising a minority of the mass (Log $M_{nuclear}/M_{\odot} =
7.3^{+0.5}_{-0.5}$ and Log $M_{outflow}/M_{\odot} \sim 6.3$) but the majority
of the luminosity (Log $L_{nuclear}/L_{\odot} = 6.90^{+0.16}_{-0.16}$ and Log
$L_{outflow}/L_{\odot} \sim 7.2$). The outflow has an anomalously high
$L_\mathrm{CO}/L_\mathrm{FIR}$ of $1.7 \times 10^{-3}$ and is almost certainly
shock excited.
