We report two designs of silicon photonic dual-drive Michelson interferometric modulators (MIMs) suitable for four-level pulse amplitude modulation (PAM-4) that do not require digital-to-analog converters or digital signal processing. The PN junctions in MIM-1 have an asymmetric geometry and 4 doping concentrations, while those in MIM-2 have a symmetric geometry and 6 doping concentrations. We simulate and experimentally demonstrate that MIM-2 has a larger modulation efficiency and a better electro-optic (EO) bandwidth than MIM-1. The measured VπLπ of MIM-2 at -2 V bias is 0.8 V-cm, and the measured 3-dB EO bandwidth at 0 V bias is 9.3 GHz. By carefully choosing the bias conditions of the device and the driving binary radio-frequency signals applied on each phase shifter, PAM-4 signals with even spacings are generated. Successful 56 Gb/s PAM-4 transmission over 2 km of standard single mode fiber is presented, with an estimated bit error rate below the hard-decision forward error correction threshold of 3.8 × 10-3.