We demonstrate that measurements of the neutral-current Drell-Yan transverse momentum distribution binned in invariant mass are sensitive to unexplored dimension-8 parameters of the Standard Model Effective Field Theory (SMEFT). These distributions are sensitive to four-fermion operators with additional QCD field strength tensors. The determination of the Wilson coefficients of these operators provides a useful diagnostic tool that distinguishes possible ultraviolet completions of the SMEFT. We study how well these effects can be probed by current LHC data, and explore the sensitivity of the future high-luminosity LHC (HL-LHC) to these operators. We find that the HL-LHC data has the potential to strongly probe this sector of the SMEFT.