Amplifier-free coherent systems are promising for short-reach links, but these systems are constrained by signal peak power instead of average power. In this paper, we propose a novel, to the best of our knowledge, quadrant-partitioning uniformly distributed modulation (QP-UDM) scheme for peak-power-constrained amplifier-free systems. The proposed scheme achieves finer modulation orders than conventional UDM schemes. It also avoids the problem in conventional amplitude-division irregular quadrature amplitude modulation, where the order of check bit sequence would be disrupted when there are errors, resulting in the failure of forward error correction decoding. When compared to probabilistic shaping (PS), the proposed QP-UDM has a lower peak-to-average-power ratio. Experiments of a 28 Gbaud amplifier-free system with the modulation order varying from 36 to 104 show that the proposed QP-UDM scheme solves the problem of conventional UDM schemes and outperforms PS-QAM at the same entropy.