In this paper we study an asymptotically optimal tame tower over the field with p(2) elements introduced by Garcia-Stichtenoth. This tower is related with a modular tower, for which explicit equations were given by Elkies. We use this relation to investigate its Galois closure. Along the way, we obtain information about the structure of the Galois closure of X-0(p(n)) over X-0(p(r)), for integers 1 < r < n and prime p and the Galois closure of other modular towers (X-0(p(n)))n.