The generator matrix 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X^2 1 1 1 1 1 1 X 1 X 1 0 1 X X^2 X 1 1 1 1 0 1 X 1 1 X^2 1 0 0 X 0 X 0 0 X X^2+X 0 X^2 X X^2+X 0 X X X^2 X^2 X^2+X X^2+X X^2 X^2+X X^2 X^2+X X^2 0 0 X^2+X X^2+X X^2+X X^2+X X^2 X^2+X X^2+X X^2 X^2 X^2 X^2 X^2 X X^2+X X^2+X X^2 0 X^2+X X^2 X X^2 X X X X^2 X 0 0 X^2+X 0 X^2+X X^2 X X^2 X X X X^2 X X X^2+X 0 0 X^2 X^2 X^2+X X 0 0 0 0 X X 0 X^2+X X 0 X^2 X X 0 0 X^2+X X^2 X^2+X X^2 X^2+X 0 X 0 0 X X^2+X X^2 X^2+X X^2+X 0 0 X^2+X X^2+X X^2 X^2 0 0 X^2+X X^2+X X^2+X X X^2+X 0 X^2+X X^2 X X^2 X 0 X 0 X^2 X X^2+X 0 X X^2 0 X^2 X^2 X^2 X^2+X X^2+X X X^2+X X^2+X X X^2+X X X X X X^2 X X 0 X 0 0 0 X^2 0 0 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 0 0 0 0 X^2 X^2 0 0 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 0 X^2 0 0 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 0 0 0 0 0 X^2 0 0 0 0 0 X^2 0 X^2 X^2 0 0 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 0 0 X^2 0 0 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 0 0 X^2 0 0 X^2 0 X^2 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 0 0 0 X^2 X^2 X^2 0 X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 0 0 X^2 0 0 X^2 0 X^2 0 0 X^2 0 X^2 0 0 X^2 0 0 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 X^2 0 X^2 0 X^2 X^2 0 X^2 0 0 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 0 0 X^2 0 0 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 0 generates a code of length 75 over Z2[X]/(X^3) who´s minimum homogenous weight is 68. Homogenous weight enumerator: w(x)=1x^0+176x^68+12x^69+81x^70+80x^71+200x^72+252x^73+81x^74+352x^75+151x^76+228x^77+54x^78+80x^79+138x^80+20x^81+30x^82+78x^84+9x^86+20x^88+1x^90+3x^92+1x^128 The gray image is a linear code over GF(2) with n=300, k=11 and d=136. This code was found by Heurico 1.16 in 6.43 seconds.