The generator matrix 1 0 0 0 1 1 1 0 1 1 X 1 X X 1 1 1 0 X 1 1 1 1 X 0 1 0 X 1 0 0 0 0 1 0 0 0 0 X X X+1 1 1 1 1 1 X 0 X+1 1 X 1 0 X+1 X+1 0 0 1 1 1 0 1 X X 0 0 1 0 0 1 1 1 0 X+1 1 X X X+1 0 X+1 X+1 X+1 1 1 1 X 0 1 0 X+1 1 1 X 1 X 0 0 0 0 1 1 X+1 0 X+1 X X 0 X+1 1 X+1 X 0 X 1 X+1 1 X+1 X 0 X 1 X+1 X 0 0 0 1 0 0 0 0 0 X X 0 X 0 0 0 X X X X X X 0 0 0 0 0 X 0 X 0 0 X X 0 0 X 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+154x^28+64x^30+131x^32+40x^34+68x^36+16x^38+28x^40+8x^42+2x^44 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 0.114 seconds.