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A binary $[98280, 24, 47104]_2$ projective two-weight code related to thesporadic simple group ${\rm Co}_1$ of Conway is constructed as a faithful andabsolutely irreducible submodule of the permutation module induced by theprimitive action of ${\rm Co}_1$ on the cosets of ${\rm Co}_2$. The dual codeof this code is a uniformly packed $[98280, 98256,3]_2$ code. The geometricsignificance of the codewords of the code can be traced to the vectors in theLeech lattice, thus revealing that the stabilizer of any non-zero weightcodeword in the code is a maximal subgroup of ${\rm Co}_1$. Similarly, thestabilizer of the codewords of minimum weight in the dual code is a maximalsubgroup of ${\rm Co}_1$. As by-product, a new strongly regular graph on16777216 vertices and valency 98280 is constructed using the codewords of thecode.

A projective two-weight code related to the simple group ${\rm Co}_1$ of Conway