We propose a coherent bidirectional link over a 4-core single-mode fiber for short-reach data center interconnects (DCIs). The proposed self-homodyne coherent link efficiently utilizes all the polarization and spatial modes in the fiber (by polarization multiplexing the carrier in two of the cores) to achieve a single-fiber full-duplex high capacity interconnect, while also providing the advantages of self-homodyning. For proof-of-the-concept, a single-lambda 13km bidirectional 40 Gbaud 16-QAM link, achieving 2×400 Gbps data rate (after 20% FEC overheads), is demonstrated. With wavelength division multiplexing and higher baud-rates, the approach can help meet the upcoming requirements for high-capacity DCIs.