Terahertz (THz) band nanocommunication is envisioned to revolutionize the future of wireless communications enabling applications in the nanoscale domains including the internet of nanothings, wireless on-chip communications, and advanced health monitoring. The communication among nanodevices, however, is hindered by the THz channel, which is highly frequency-selective and distance-dependent in nature, ultimately restricting the nanocommunication distances to a few millimeters. Moreover, multiple nano-devices trying to access the channel simultaneously increase interference in the overall communication system. This paper proposes a new pulse-based modulation for nanonetworks called multi-level pulse position modulation (ML-PPM) and analyzes its performance in the multiuser nanocommunication scenario. In ML-PPM, each nanomachine in the nanonetwork first transforms the transmitting bits into multi-levels by using several orthogonal codes, and then, each multi-level is modulated as a pulse position. The ML-PPM signal thus generated is subsequently time-hopped to achieve multiple access. As a consequence of employing orthogonal coding, the spreading gain is achieved at the nanoreceiver, which improves the performance of the proposed scheme. The time-hopped multilevel PPM scheme is evaluated in terms of bit error rate (BER) and link capacity, for different THz propagation conditions and different system design parameters. The results show that for a THz channel concentrated with 10% water vapor, a link capacity of approximately 1 Gigabits-per-second is achieved for a transmission distance of 0.5mm.