  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. This configuration is isomorphic to the configuration of points and lines
on the projective plane over the finite field of 4 elements. The surface admits
a finite automorphism group which contains the group of automorphisms of the
plane which acts on the configuration of each set of 21 smooth rational curves,
and the additional element of order 2 which interchanges the two sets. The
Picard lattice of the surface is a reflective sublattice of an even unimodular
lattice of signatuire (1,25) and the classes of the 42 curves correspond to
some Leech roots in this lattice.
