Information exchange requires a measurement of physical states. Because quantum measurements enable accuracy beyond the classical shot-noise limit, they are successfully used to develop measurement tools and applications. In particular, quantum-measurement-enhanced strategies are used for the discrimination of nonorthogonal coherent states. The efficient discrimination of these states is crucial for optical communication networks, that are now approaching the classical limits of the underlying physical systems. However, quantum-enhanced discrimination strategies demonstrated to date are based on legacy communication protocols designed for classical measurements and thus provide only a limited advantage. In our work, we use photon detection times readily available in quantum measurement, but not accessible by classical means. We measure and use these times to maximize our knowledge about faint nonorthogonal coherent states. We employ communication strategies designed to benefit most from this knowledge. This holistic approach in our experiment has resulted in the record low error rates in discrimination of multiple faint nonorthogonal coherent states carrying energy corresponding to just one photon per bit of transmitted information. We demonstrate successful discrimination of large alphabets of optical states (4 <= M <= 16) beyond the ideal classical shot-noise limit, showing the scalability of quantum-measurement-enabled communication. This experimental work explores unforeseen advantages of quantum measurement on one hand, and may help address the capacity crunch in modern optical networks caused by the exponential growth of data exchange on the other.