  While a propagating state of light can be generated with arbitrary squeezing
by pumping a parametric resonator, the intra-resonator state is limited to 3 dB
of squeezing. Here, we implement a reservoir engineering method to surpass this
limit using superconducting circuits. Two-tone pumping of a three-wave-mixing
element implements an effective coupling to a squeezed bath which stabilizes a
squeezed state inside the resonator. Using an ancillary superconducting qubit
as a probe allows us to perform a direct Wigner tomography of the
intra-resonator state. The raw measurement provides a lower bound on the
squeezing at about $6.7 \pm 0.2$ dB below the zero-point level. Further, we
show how to correct for resonator evolution during the Wigner tomography and
obtain a squeezing as high as $8.2 \pm 0.8$ dB. Moreover, this level of
squeezing is achieved with a purity of $-0.4 \pm 0.4$ dB.
