The generator matrix 1 0 0 1 1 1 X 1 1 X 1 0 0 1 1 1 0 1 1 0 1 1 0 0 1 1 0 0 X X X X X 1 X 1 0 0 1 1 0 1 1 X 0 1 1 X 1 0 X 1 0 X 1 1 1 0 1 1 1 0 1 X X X X 1 1 1 1 1 1 1 0 1 0 0 1 X+1 1 0 1 1 X+1 1 0 0 X X+1 1 X X+1 1 X 1 1 X X 1 1 X 1 1 1 1 1 X 1 1 1 1 X 1 1 0 X 1 1 0 X+1 1 X+1 1 1 X 0 1 X+1 0 1 0 0 X X+1 1 1 X 0 X 0 0 X X 0 X 0 0 0 0 1 1 1 0 1 X X+1 X+1 X X 1 X+1 X X+1 X+1 0 1 1 1 X 0 1 X+1 0 X 1 1 X+1 1 X+1 1 1 X+1 1 X+1 0 X+1 X+1 X X+1 X X 1 1 X+1 0 1 0 X X X 0 0 0 0 0 X 0 X X X X 0 X X X X 1 X+1 1 X X+1 0 0 0 X 0 0 0 0 0 0 0 0 0 X X X X X X X 0 X X X 0 X X X X X 0 0 X 0 X 0 0 X 0 0 X 0 X X 0 0 0 X 0 0 0 0 X 0 0 X 0 X X X 0 0 0 X X X X X 0 X 0 X X 0 0 0 0 0 X X 0 X 0 X 0 X X X X 0 0 0 X X 0 0 0 0 X X X X X 0 X 0 0 X X 0 X X 0 X 0 0 0 X 0 X X 0 0 X 0 0 X X 0 X 0 0 0 X X 0 X 0 X X X X X X X 0 0 0 generates a code of length 74 over Z2[X]/(X^2) who´s minimum homogenous weight is 72. Homogenous weight enumerator: w(x)=1x^0+184x^72+32x^76+22x^80+16x^88+1x^96 The gray image is a linear code over GF(2) with n=148, k=8 and d=72. As d=72 is an upper bound for linear (148,8,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 8. This code was found by Heurico 1.16 in 12.2 seconds.