Summary: 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 \(\mathbb{C}^3\otimes\mathbb{C}^6\otimes\mathbb{C}^6\) 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.