We construct a K3 surface over an algebraically closed field of characteristic 2 which contains two sets of 21 disjoint smooth rational curves such that each curve from one set intersects exactly 5 curves from the other set. We also give a description of the group of automorphisms of the K3 surface, and a relation with an even definite unimodular lattice of rank 24 called the Leech lattice. This is joint work with I. Dolgachev and T. Katsura.