This study investigates the potential of long-wave infrared (LWIR) free-space optical (FSO) transmission using multilevel signals to achieve high spectral efficiency. The FSO transmission system includes a directly modulated-quantum cascade laser (DM-QCL) operating at 9.1 µm and a mercury cadmium telluride (MCT) detector. The laser operated at the temperature settings of 15°C and 20°C. The experiment was conducted over a distance of 1 m and in a lab as a controlled environment. We conduct small-signal characterization of the system, including the DM-QCL chip and MCT detector, evaluating the end-to-end response of both components and all associated electrical elements. For large-signal characterization, we employ a range of modulation formats, including non-return-to-zero on-off keying (NRZ-OOK), 4-level pulse amplitude modulation (PAM4), and 6-level PAM (PAM6), with the objective of optimizing both the bit rate and spectral efficiency of the FSO transmission by applying pre- and post-processing equalization. At 15°C, the studied LWIR FSO system achieves net bitrates of 15 Gbps with an NRZ-OOK signal and 16.9 Gbps with PAM4, both below the 6.25% overhead hard decision-forward error correction (6.25%-OH HD-FEC) limit, and 10 Gbps NRZ-OOK below the 2.7% overhead Reed-Solomon RS(528,514) pre-FEC (KR-FEC limit). At 20°C, we obtained net bitrates of 14.1 Gbps with NRZ-OOK, 16.9 Gbps with PAM4, and 16.4 Gbps with PAM6. Furthermore, we evaluate the BER performance as a function of the decision feedback equalization (DFE) tap number to explore the role of equalization in enhancing signal fidelity and reducing errors in FSO transmission. Our findings accentuate the competitive potential of DM-QCL and MCT detector-based FSO transceivers with digital equalization for the next generation of FSO communication systems.