  We report the discovery of shocked molecular and ionized gas resulting from
jet-driven feedback in the compact radio galaxy 4C 31.04 using near-IR imaging
spectroscopy. 4C 31.04 is a $\sim 100$ pc double-lobed Compact Steep Spectrum
source believed to be a very young AGN. It is hosted by a giant elliptical with
a $\sim 10^{9}~\rm M_\odot$ multi-phase gaseous circumnuclear disc. We used
high spatial resolution, adaptive optics-assisted $H$- and $K$-band integral
field Gemini/NIFS observations to probe (1) the warm ($\sim 10^3~\rm K$)
molecular gas phase, traced by ro-vibrational transitions of $\rm H_2$, and
(2), the warm ionized medium, traced by the [Fe II]$_{1.644~\rm \mu m}$ line.
The [Fe II] emission traces shocked gas ejected from the disc plane by a
jet-blown bubble $300-400~\rm pc$ in diameter, whilst the $\rm H_2$ emission
traces shock-excited molecular gas in the interior $\sim 1~\rm kpc$ of the
circumnuclear disc. Hydrodynamical modelling shows that the apparent
discrepancy between the extent of the shocked gas and the radio emission can
occur when the brightest regions of the synchrotron-emitting plasma are
temporarily halted by dense clumps, whilst less bright plasma can percolate
through the porous ISM and form an energy-driven bubble that expands freely out
of the disc plane. This bubble is filled with low surface-brightness plasma not
visible in existing VLBI observations of 4C 31.04 due to insufficient
sensitivity. Additional radial flows of jet plasma may percolate to $\sim \rm
kpc$ radii in the circumnuclear disc, driving shocks and accelerating clouds of
gas, giving rise to the $\rm H_2$ emission.
