The generator matrix 1 0 1 1 1 0 1 1 0 1 1 0 1 1 0 1 1 1 0 1 1 X 1 1 X 1 1 1 1 1 1 1 0 1 1 0 1 1 0 X+1 1 0 X+1 1 X+1 0 1 X 0 X+1 1 0 1 1 X 1 1 0 0 X 0 X X X 0 0 X 0 0 0 0 0 0 X 0 X 0 X X X 0 X 0 X X X X X X X X X 0 X X 0 0 0 0 X 0 0 0 X 0 X X 0 0 X 0 0 X X X X 0 X 0 X 0 X 0 0 0 X X 0 0 0 0 0 X 0 0 0 X 0 X X X 0 0 0 0 X 0 X X 0 X X 0 X 0 X X 0 0 X 0 0 0 0 0 X 0 X X 0 X 0 0 X X X X 0 0 X X 0 0 X X 0 0 0 0 X 0 X 0 0 0 0 0 0 X X 0 X X 0 X 0 X X 0 X 0 0 X X 0 X 0 0 0 X X X 0 0 generates a code of length 32 over Z2[X]/(X^2) who´s minimum homogenous weight is 28. Homogenous weight enumerator: w(x)=1x^0+184x^28+157x^32+160x^36+8x^44+2x^48 The gray image is a linear code over GF(2) with n=64, k=9 and d=28. As d=28 is an upper bound for linear (64,9,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 9. This code was found by Heurico 1.16 in 33.9 seconds.