Before revision: We show that computing the Tutte polynomial of a linear matroid of dimension k on k^{O(1)} points over a field of k^{O(1)} elements requires k^{\Omega(k)} time unless the  ETH---a counting extension of the Exponential Time Hypothesis of Impagliazzo and Paturi [CCC 1999] due to Dell {\em et al.
After revision: We show that computing the Tutte polynomial of a linear matroid of dimension k on k^{O(1)} points over a field of k^{O(1)} elements requires k^{\Omega(k)} time unless the \# ETH---a counting extension of the Exponential Time Hypothesis of Impagliazzo and Paturi [CCC 1999] due to Dell {\em et al.