Understanding gas flow is essential for developing galaxy formation and evolution models. However, mapping galactic-scale outflows is difficult to accomplish at high redshifts due to the innate low surface brightness of emitting gas. Using very deep observations of the Hubble Deep Field South (HDFS) with the Multi Unit Spectroscopic Explorer (MUSE) on the Very Large Telescope (VLT), we detect some signatures of outflow in emission and absorption for 10 spatially resolved galaxies using resonantly-scattered MgII 2796, 2803, within a redshift range of 0.8 < z < 1.4. We identify outflow in MgII emission with a 4σ surface brightness detection of (6.3 ± 1.8) × 10−21 erg cm−2 s −1 arcsec−2, extending to 15 kpc, in a galaxy at z = 1.284. We place 3σ surface brightness limits for our nine other galaxies, with the least sensitive being 2.8 × 10−21 erg cm−2 s −1 arcsec−2. These measurements coupled with star formation rate and stellar mass data, provide us with the opportunity to understand the kinematics and morphology of galactic winds in our sample of galaxies. By creating flux versus radius plots, we demsonstrate that our confidently detected galaxy with outflows has Mg II emission extending beyond the galaxy’s stellar component.