We experimentally demonstrate the enhanced atmospheric turbulence resiliency in a 137.8 Gbit/s/mode mode-division multiplexing free-space optical communication link through the application of a successive interference cancellation digital signal processing algorithm. The turbulence resiliency is further enhanced through redundant receive channels in the mode-division multiplexing link. The proof of concept demonstration is performed using commercially available mode-selective photonic lanterns, a commercial transponder, and a spatial light modulator based turbulence emulator. In this link, 5 spatial modes with each mode carrying 34.46 GBaud dual-polarization quadrature phase shift keying signals are successfully transmitted with an average bit error rate lower than the hard-decision forward error correction limit. As a result, we achieved a record-high mode- and polarization-division multiplexing channel number of 10, a record-high line rate of 689.23 Gbit/s, and a record-high net spectral efficiency of 13.9 bit/s/Hz in emulated turbulent links in a mode-division multiplexing free-space optical system.