In this paper we will demonstrate that a computational system can meet the criteria for autonomy laid down by classical enactivism. The two criteria that we will focus on are operational closure and structural determinism, and we will show that both can be applied to a basic example of a physically instantiated Turing machine. We will also address the question of precariousness, and briefly suggest that a precarious Turing machine could be designed. Our aim in this paper is to challenge the assumption that computational systems are necessarily heteronomous systems, to try and motivate in enactivism a more nuanced and less rigid conception of computational systems, and to demonstrate to computational theorists that they might find some interesting material within the enactivist tradition, despite its historical hostility towards computationalism.