The generator matrix 1 0 0 0 1 1 1 X 1 1 X 1 1 0 X 1 0 1 X 1 0 1 0 1 X 1 X 1 1 1 1 0 X 1 1 1 1 X 1 1 1 0 1 0 1 X 0 X 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 X 1 1 1 X 1 1 1 0 1 0 0 0 0 0 0 1 X+1 1 1 X+1 1 1 X X X+1 1 X+1 1 X X X+1 1 1 1 0 X X X+1 1 0 0 X X+1 X+1 0 X+1 X+1 X+1 X X 1 1 1 1 1 X+1 X X 0 0 1 1 X+1 X+1 0 X+1 X 0 0 X X 1 1 1 1 0 0 0 X 0 0 1 0 0 1 X+1 1 1 X+1 0 0 0 1 1 0 0 0 0 X X X+1 1 1 X+1 X X X X+1 1 1 X+1 1 X 1 0 X+1 1 X+1 X X 1 1 0 1 0 X+1 1 1 X+1 X 0 0 X+1 X+1 X+1 1 X 1 X X+1 X 0 0 X 0 1 X X 1 X 0 0 0 0 1 1 X+1 0 X+1 0 1 X+1 X+1 0 X+1 0 1 1 X+1 1 X X 0 0 0 0 X X X 1 X+1 1 X+1 1 0 X+1 X X+1 X+1 X+1 0 0 X+1 1 0 X 1 X X 0 X 1 X+1 X X X+1 X X X 1 0 0 X+1 X+1 1 0 1 0 X 1 X+1 0 X 0 0 0 0 X X X 0 X X 0 X X 0 0 0 X 0 X 0 X 0 X 0 X 0 X X X X 0 X X X 0 X X X 0 X 0 0 0 X 0 0 0 X X X X 0 X X 0 0 X 0 X X 0 0 0 X 0 X 0 X 0 0 0 0 generates a code of length 72 over Z2[X]/(X^2) who´s minimum homogenous weight is 68. Homogenous weight enumerator: w(x)=1x^0+221x^68+165x^72+62x^76+30x^80+21x^84+9x^88+3x^96 The gray image is a linear code over GF(2) with n=144, k=9 and d=68. As d=68 is an upper bound for linear (144,9,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 9. This code was found by Heurico 1.16 in 10.9 seconds.