The Weyl semimetal $\mathrm{Mo}{\mathrm{Te}}_{2}$ offers a rare opportunity to study the interplay between Weyl physics and superconductivity. Recent studies have found that Se substitution can boost the superconductivity up to 1.5 K, but suppresses the ${T}_{d}$ structure phase that is essential for the emergence of the Weyl state. A microscopic understanding of the possible coexistence of enhanced superconductivity and the ${T}_{d}$ phase has not been established so far. Here, we use scanning tunneling microscopy to study an optimally doped superconductor $\mathrm{Mo}{\mathrm{Te}}_{1.85}{\mathrm{Se}}_{0.15}$ with bulk ${T}_{c}\ensuremath{\sim}1.5\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. By means of quasiparticle interference imaging, we identify the existence of a low-temperature ${T}_{d}$ phase with broken inversion symmetry where superconductivity globally coexists. Furthermore, we find that the superconducting coherence length, extracted from both the upper critical field and the decay of density of states near a vortex, is much larger than the characteristic length scale of the existing chemical disorder. Our findings of robust superconductivity arising from a Weyl semimetal normal phase in $\mathrm{Mo}{\mathrm{Te}}_{1.85}{\mathrm{Se}}_{0.15}$ make it a promising candidate for realizing topological superconductivity.