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We present a blind time-delay cosmographic analysis for the lens system DESJ0408$-$5354. This system is extraordinary for the presence of two sets ofmultiple images at different redshifts, which provide the opportunity to obtainmore information at the cost of increased modelling complexity with respect topreviously analyzed systems. We perform detailed modelling of the massdistribution for this lens system using three band Hubble Space Telescopeimaging. We combine the measured time delays, line-of-sight central velocitydispersion of the deflector, and statistically constrained external convergencewith our lens models to estimate two cosmological distances. We measure the"effective" time-delay distance corresponding to the redshifts of the deflectorand the lensed quasar $D_{\Delta t}^{\rm eff}=3382^{+146}_{-115}$ Mpc and theangular diameter distance to the deflector $D_{\rm d}=1711^{+376}_{-280}$ Mpc,with covariance between the two distances. From these constraints on thecosmological distances, we infer the Hubble constant $H_0 = 74.2^{+2.7}_{-3.0}$km s$^{-1}$ Mpc$^{-1}$ assuming a flat $\Lambda$CDM cosmology and a uniformprior for $\Omega_{\rm m}$ as $\Omega_{\rm m} \sim \mathcal{U}(0.05, 0.5)$.This measurement gives the most precise constraint on $H_0$ to date from asingle lens. Our measurement is consistent with that obtained from the previoussample of six lenses analyzed by the $H_0$ Lenses in COSMOGRAIL's Wellspring(H0LiCOW) collaboration. It is also consistent with measurements of $H_0$ basedon the local distance ladder, reinforcing the tension with the inference fromearly Universe probes, for example, with 2.2$\sigma$ discrepancy from thecosmic microwave background measurement.

STRIDES: a 3.9 per cent measurement of the Hubble constant from the strong lens system DES J0408-5354