The generator matrix 1 0 0 1 1 1 X^2+X X 1 1 1 X^2 X^2 1 0 1 1 1 X 0 1 X^2 X^2+X 1 1 1 1 X X^2+X 1 X^2 1 X 1 1 1 1 X^2 X^2+X 1 1 0 0 1 1 X^2+X 1 1 X^2 X^2+X 1 1 1 X 1 1 1 1 X 1 1 1 X 0 1 X 1 1 X^2 1 0 1 1 1 1 1 0 1 1 X^2 X 1 X X 1 X^2+X 1 1 1 0 1 0 0 1 X+1 1 X^2 X^2+X+1 X+1 X^2+X 1 1 X^2 0 0 X^2+1 X 1 1 1 1 0 X X^2+X+1 X^2+1 X^2+X 1 X 1 1 X^2+X 1 X 1 X^2 X^2+X 1 1 1 X^2 0 1 X+1 X 1 X^2+X+1 X X^2+X 1 X+1 X^2 X^2+1 X 0 X+1 X^2 X^2+X+1 1 X^2+1 X^2+X 0 X^2 1 0 1 X^2+X+1 X+1 1 X+1 X X X^2+X+1 X^2+1 X+1 X^2+X+1 1 1 X^2+1 1 X^2+X X^2+X+1 1 1 X 1 X^2+X+1 X^2+X+1 0 0 0 1 1 1 X^2 1 1 X+1 X^2+X X^2+1 X^2+1 X^2+X X 1 X^2 1 1 1 X^2 X^2 1 1 X+1 X^2+X X^2+X+1 X^2 0 1 0 X+1 X^2 0 X^2+X+1 X^2+X+1 X+1 X^2+X X X^2+X+1 X X^2+X 1 X^2 X^2+X X^2+X+1 1 X+1 X^2+1 1 X X X^2+X+1 0 1 0 0 X X^2+1 X^2+X X^2+1 X^2+X 1 1 X^2+X+1 X^2+X X^2+X+1 0 0 X+1 X^2+X+1 1 X^2+1 X^2+X+1 X^2+X X^2+1 X+1 X 0 X^2+X+1 1 1 X+1 1 X^2+X+1 X 1 X^2+1 1 X^2 0 0 0 X X^2+X 0 X X X^2+X 0 X^2+X X^2+X 0 0 X^2+X X^2+X X^2 0 X^2 X^2+X X X^2 0 0 X^2 X^2 X X X^2 X^2 X X^2 0 X X^2+X X X 0 0 X^2 X^2+X 0 0 X^2+X X^2 X 0 0 X X^2+X X X^2 X X 0 X X^2+X X X^2 X^2+X X^2 X^2 X^2 X^2 X^2 X X^2+X X^2 X^2 X^2 X^2+X X X X X^2+X X^2+X X^2+X X^2+X 0 0 X X 0 X^2 X^2+X X^2+X 0 X^2 X^2 0 0 0 0 X^2 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 X^2 X^2 0 0 0 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 0 0 X^2 0 X^2 X^2 X^2 0 0 0 0 0 X^2 0 X^2 0 0 0 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 generates a code of length 89 over Z2[X]/(X^3) who´s minimum homogenous weight is 82. Homogenous weight enumerator: w(x)=1x^0+66x^82+208x^83+381x^84+288x^85+466x^86+380x^87+390x^88+236x^89+331x^90+296x^91+229x^92+156x^93+204x^94+92x^95+97x^96+56x^97+69x^98+32x^99+42x^100+28x^101+14x^102+16x^103+4x^104+4x^105+6x^108+2x^110+2x^112 The gray image is a linear code over GF(2) with n=356, k=12 and d=164. This code was found by Heurico 1.16 in 1.49 seconds.