We report on a subpercent scale determination using the omega baryon mass and gradient-flow methods. The calculations are performed on 22 ensembles of Nf=2+1+1 highly improved, rooted staggered sea-quark configurations generated by the MILC and CalLat Collaborations. The valence quark action used is Möbius domain wall fermions solved on these configurations after a gradient-flow smearing is applied with a flowtime of tgf=1 in lattice units. The ensembles span four lattice spacings in the range 0.06≲a≲0.15 fm, six pion masses in the range 130≲mπ≲400 MeV and multiple lattice volumes. On each ensemble, the gradient-flow scales t0/a2 and w0/a and the omega baryon mass amΩ are computed. The dimensionless product of these quantities is then extrapolated to the continuum and infinite volume limits and interpolated to the physical light, strange and charm quark mass point in the isospin limit, resulting in the determination of t0=0.1422(14) fm and w0=0.1709(11) fm with all sources of statistical and systematic uncertainty accounted for. The dominant uncertainty in both results is the stochastic uncertainty, though for t0 there are comparable continuum extrapolation uncertainties. For w0, there is a clear path for a few-per-mille uncertainty just through improved stochastic precision, as recently obtained by the Budapest-Marseille-Wuppertal Collaboration.