We experimentally demonstrate a net capacity per wavelength of 1.23 Tb/s with 30 GBaud 16-ary quadrature amplitude modulation (16-QAM) mode-division multiplexing (MDM) signals over a single silicon-on-insulator (SOI) multimode waveguide for optical interconnects employing $11 \times 11$ multiple-in-multiple-out (MIMO) digital signal processing. In order to simplify the receiver architecture for coherent optical interconnects, we further propose and evaluate an on-chip self-homodyne coherent detection (SHCD) scheme. In the experiment, 30 Gbaud quadrature phase shift keying (QPSK) signals carried by 10 waveguide modes are successfully recovered with bit error rates (BERs) below 7% forward error correction (FEC) threshold using the pilot tone delivered by ${{\rm TE}_0}$ mode as a local oscillator. Around 10% penalty on error vector magnitude (EVM) is observed due to modal cross talk compared to homodyne detection.