Weight enumerators of extremal singly-even [60,30,12] codes

Conway and Sloane (1990) have listed the possible weight enumerators for extremal self-dual codes up to length 72. In this correspondence, we construct extremal singly-even self-dual [60,30,12] codes whose weight enumerator does not appear in this list. In addition, we present the possible weight enumerators for extremal self-dual codes of length 60.