  The identifiability of parameters in a probabilistic model is a crucial
notion in statistical inference. We prove that a general tensor of rank 8 in
C^3\otimes C^6\otimes C^6 has at least 6 decompositions as sum of simple
tensors, so it is not 8-identifiable. This is the highest known example of
balanced tensors of dimension 3, which are not k-identifiable, when k is
smaller than the generic rank.
