  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 SMM, which allowed the
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 Tb2-SMM via single crystal {\mu}-SQUID
measurements at sub-Kelvin temperatures. We observe ferromagnetic interactions
between the Tb(III) ions and cooperative quantum tunneling of the electronic
spins with spin ground state \textit{J} = {\pm}6. The 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 to read-out the Tb(III) nuclear spin
states via the cooperative tunneling of the electronic spins, making the
dimeric Tb2-SMM an excellent nuclear spin qudit candidate with d =16.
