  Recent high-$z$ quasar observations strongly indicate that super-Eddington
accretion is a crucial phase to describe the existence of supermassive black
holes (SMBHs) with $M_\mathrm{BH} \gtrsim 10^9 M_\odot$ at $z \gtrsim 7$.
Motivated by the theoretical suggestion that the super-Eddington phase
efficiently produces outflows and jets bright in radio bands, we search and
find a super-Eddington radio-loud dust-obscured galaxy (DOG) J1406+0102 at
$z=0.236$, through cross-matching of the infrared-bright DOGs of Noboriguchi et
al. (2019) with the VLA/FIRST 1.4 GHz radio and the SDSS optical spectral
catalog. DOG J1406+0102 shows broad components in the Balmer lines. Assuming
those lines are from the broad line region, it gives BH mass estimation of
$\log\ (M_\mathrm{BH}/M_\odot)=7.30 \pm 0.25$, and AGN luminosity of $\log
(L_\mathrm{bol,[OIII]}/\mathrm{erg}~\mathrm{s}^{-1})
  = 45.91\pm0.38$ estimated from the intrinsic [OIII] luminosity, resulting in
super-Eddington accretion of $\lambda_\mathrm{Edd}\simeq 3$. We show that 1)
DOG J1406+0102 is operating strong AGN feedback: the [OIII] outflow velocity
exceeds the escape velocity of the host galaxy halo and the kinetic efficiency
is obtained as $\approx$ 8% that can be sufficient to quench the host galaxy,
2) the expected future growth pathway of DOG J1406+0102 would join an
over-massive BH trajectory and 3) radio-loud DOGs can provide a significant
contribution to the high-energy ($\gtrsim$ 100 TeV) cosmic neutrino background
if we assume DOG J1406+0102 as a representative of radio-loud DOGs.
