  We present the lens mass model of the quadruply-imaged gravitationally lensed
quasar WFI2033-4723, and perform a blind cosmographical analysis based on this
system. Our analysis combines (1) time-delay measurements from 14 years of data
obtained by the COSmological MOnitoring of GRAvItational Lenses (COSMOGRAIL)
collaboration, (2) high-resolution $\textit{Hubble Space Telescope}$ imaging,
(3) a measurement of the velocity dispersion of the lens galaxy based on
ESO-MUSE data, and (4) multi-band, wide-field imaging and spectroscopy
characterizing the lens environment. We account for all known sources of
systematics, including the influence of nearby perturbers and complex
line-of-sight structure, as well as the parametrization of the light and mass
profiles of the lensing galaxy. After unblinding, we determine the effective
time-delay distance to be $4784_{-248}^{+399}~\mathrm{Mpc}$, an average
precision of $6.6\%$. This translates to a Hubble constant $H_{0} =
71.6_{-4.9}^{+3.8}~\mathrm{km~s^{-1}~Mpc^{-1}}$, assuming a flat $\Lambda$CDM
cosmology with a uniform prior on $\Omega_\mathrm{m}$ in the range [0.05, 0.5].
This work is part of the $H_0$ Lenses in COSMOGRAIL's Wellspring (H0LiCOW)
collaboration, and the full time-delay cosmography results from a total of six
strongly lensed systems are presented in a companion paper (H0LiCOW XIII).
