Nanomachines are submicrometer-scale devices led by nanotechnology that can perform simple sensing, local actuation, limited data processing, storage, and communication tasks in the terahertz (THz) band, that is, from 0.1-10 THz. Electromagnetic nanocommunication among nanomachines results in a nanonetwork which could breakthrough promising applications in multiple domains such as software-defined metamaterials, in-body communication, and on-chip communication. This study adopts a modulation scheme for nanomachine communication based on multilevel pulse position modulation (ML-PPM). The multilevel scheme uses several orthogonal codes and is combined with PPM to generate the final transmit signal consisting of several multilevels. In this paper, we propose a more advanced scheme called level trimming to further boost the data rates of the ML-PPM scheme. Employing level-trimming, we transmit a fewer number of levels than required in ML-PPM, which will results in an spectral efficiency gain at the nanoreceiver. The simulation results reveal that the link capacity of the proposed scheme can be increased more than twofold using the level-trimming approach while the error rate performance remains better than the conventional ML-PPM. Moreover, the computational complexity of transceivers is reduced with the transmission of fewer levels, which is a significant necessity in nanocommunication. Also, although level-trimming causes artificial errors, it also improves the decoding performance by reducing the number of levels. We believe that the potential impact of this study will open doors for further investigations on various possible modulation formats for THz nanocommunication.