As an extension of two-level quantum bits (qubits), multilevel systems, so-called qudits, where d represents the Hilbert space dimension, have been predicted to reduce the number of iterations in quantum-computation algorithms. This has been tested in the well-known [TbPc2](0) single-molecule magnet (SM_M), which allowed implementation of the Grover algorithm in a single molecular unit. In the quest for molecular systems possessing an increased number of accessible nuclear spin states, we explore herein a dimeric Tb-2-SMM via single-crystal mu-SQUID measurements at sub-Kelvin temperatures. We observe ferromagnetic interactions between the TbOIII ions and cooperative quantum tunneling of the electronic spins with spin ground state IJ(Z) = +/-6). Strong hyperfine coupling with the Tb-III nuclear spins leads to a multitude of spin-reversal paths, leading to seven strong hyperfine driven tunneling steps in the hysteresis loops. Our results show the possibility of reading out the Tb1II nuclear spin states via cooperative tunneling of the electronic spins, making the dimeric Tb2-SMM an excellent nuclear spin qudit candidate with d = 16.