Extensions of the Isometry Group of the Torus

Let $G$ be a subgroup of the group of diffeomorphisms of the torus ${\mathbb{T}}^{2}=\mathbb{R}}^{2}/{\mathbb{Z}}^{2}$. Suppose that the group of orientation preserving isometries of ${\mathbb{T}}^{2}$ is a proper subgroup of $G$,  and that $G$ contains a $C^1$ diffeomorphism, say $h$, isotopic to the identity and preserving the Lebesgue measure. Assume also that $h$ is not an isometry. Then  there exists an element $f\in G$ with positive topological entropy