The generator matrix 1 0 0 0 1 1 1 0 1 1 1 1 0 0 0 X 1 1 1 1 1 0 1 0 1 1 0 0 0 0 0 0 X X X X X X X X X X 1 1 1 1 1 X 1 1 X X 1 X 1 1 1 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 X 0 0 1 0 X X X 0 1 1 1 1 1 0 1 0 0 X 1 X+1 1 0 1 X X+1 1 X 1 1 0 1 0 1 X 1 X+1 0 X X+1 1 0 0 1 X 1 1 X 1 1 0 1 X 0 1 1 0 X+1 X+1 0 X 1 X+1 X 0 X 1 1 0 X X 1 X 0 1 X+1 X 1 X+1 0 X X+1 1 1 X+1 0 1 1 0 1 1 0 X 1 X X 0 X 0 1 0 0 1 0 0 0 0 X 1 1 1 1 X+1 1 1 0 X X X+1 X+1 X X+1 X 1 X+1 X+1 X 1 X X+1 1 1 X X 0 X X X 0 1 0 0 X+1 0 1 X 1 1 X+1 0 0 1 X+1 X+1 1 X X+1 1 X+1 0 1 0 0 X X 1 0 X 1 X+1 0 X X+1 0 1 0 X 1 1 1 X X X+1 0 1 0 0 0 0 1 1 X+1 X X+1 X+1 0 X 1 X 1 X+1 1 X 1 1 X X+1 1 0 X 0 X+1 X 1 1 0 X+1 X 0 1 0 X+1 1 X 1 1 X+1 X 0 0 X+1 X+1 0 X 1 X 1 X+1 X+1 0 X 0 X+1 0 X X 1 1 0 X+1 1 0 1 X+1 X+1 1 X+1 0 X X X+1 1 0 X+1 1 0 1 X X X+1 1 0 generates a code of length 86 over Z2[X]/(X^2) who´s minimum homogenous weight is 84. Homogenous weight enumerator: w(x)=1x^0+142x^84+86x^88+26x^92+1x^128 The gray image is a linear code over GF(2) with n=172, k=8 and d=84. As d=84 is an upper bound for linear (172,8,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 8. This code was found by Heurico 1.16 in 12 seconds.