It is well known that the extended binary Golay 124, 12, 81 code yields 5-designs. In particular, the supports of all the weight 8 codewords in the code form a Steiner system S(5, 8,24). In this paper, we give a construction of mutually disjoint Steiner systems S(5, 8, 24) by constructing isomorphic Golay codes. As a consequence, we show that there exists at least 22 mutually disjoint Steiner systems S(5, 8, 24). Finally, we prove that there exists at least 46 mutually disjoint 5-(48, 12, 8) designs from the extended binary quadratic residue 148, 24, 121 code. (C) 2009 Published by Elsevier Inc.