The generator matrix 1 0 1 1 1 X^3+X^2+X 1 1 X^3 1 1 X^2+X 1 1 X 1 X^3+X^2 1 1 X^2 1 1 1 X^3+X 1 1 X^2+X 1 1 X^3+X^2+X X^3 1 1 1 1 X^2 1 1 0 1 1 X^3+X^2 X^3+X 1 1 X 1 1 X^3 1 X^2 X 1 1 1 1 X^3+X X 1 0 1 X^2+X 1 X 1 1 X^2 1 1 X^3 1 1 X^3+X 1 X^3+X^2+X X^3+X^2+X X X^2 1 1 1 1 1 1 1 X^3+X 1 X^3+X^2+X X^3 X^2 1 0 1 X+1 X^3+X^2+X X^2+1 1 X^3+X^2+1 0 1 X^3+X^2+X X+1 1 X^3+X^2 X^2+X+1 1 X 1 1 X^3+X^2+X+1 1 X^3+X^2 X X^3+1 1 X^3 X^3+X+1 1 X^2+X X^3+1 1 1 X+1 X^3+X X^3+X^2 X^3+1 1 X^2+X+1 X^3+X^2+1 1 X X^3 1 1 X^3+X^2 X^3+X^2+1 1 X^2+X+1 X^3+X X X^2 1 1 X^2+1 X^2 X X+1 1 X^3+X^2 X^3+X^2 1 X^3+X+1 1 X^3+X^2+1 1 X^3+X^2+X+1 X^3+X^2+X 1 X^3 1 1 X^3+1 X+1 1 X^2+X+1 1 1 X^3+X^2+X 1 X^3+X^2+X X^3+1 X^3+X^2 X^3+X^2+X X^2+X 0 X+1 1 X^3+X+1 1 1 X X^3+X 0 0 X^2 0 0 0 0 X^3+X^2 X^3+X^2 X^2 X^3+X^2 X^2 X^2 X^3+X^2 X^3 X^3+X^2 X^3 X^3 X^2 X^2 X^3 X^3 X^3 X^3+X^2 0 0 X^3 X^3+X^2 X^2 X^3+X^2 0 0 X^3 X^2 X^2 X^2 X^3 X^3+X^2 X^3+X^2 0 X^3+X^2 X^3 X^2 X^3 X^3+X^2 0 X^3 X^2 X^3+X^2 X^3+X^2 0 X^3+X^2 X^3 0 0 X^2 X^2 X^3+X^2 X^3+X^2 X^3 X^3 X^2 X^2 X^3 X^2 X^3+X^2 X^3+X^2 X^3 X^3 0 0 0 X^3 0 X^3+X^2 X^3 X^3+X^2 X^2 X^3 X^2 X^3+X^2 X^3 X^3 X^3 X^3 X^2 0 0 X^2 X^2 X^2 0 0 0 X^3+X^2 X^3 X^3+X^2 X^2 X^2 X^3 X^3 X^3+X^2 X^3+X^2 X^2 0 X^3+X^2 X^3 0 X^2 X^3+X^2 X^3 0 X^3+X^2 X^3 X^3+X^2 X^2 X^3+X^2 0 X^3+X^2 X^2 X^3 X^3+X^2 X^3 0 0 X^3 X^2 0 0 X^3+X^2 X^3 X^3 X^2 0 X^3+X^2 X^3+X^2 X^3 X^2 X^2 0 X^3 0 X^3 X^3 0 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^2 X^2 X^2 0 X^3 X^3 0 0 X^2 X^3 X^3+X^2 X^3 0 0 X^2 X^3 X^2 X^3+X^2 X^2 X^3+X^2 X^3 0 0 0 X^2 0 X^3+X^2 X^3 X^2 X^2 X^2 X^2 X^3+X^2 generates a code of length 91 over Z2[X]/(X^4) who´s minimum homogenous weight is 86. Homogenous weight enumerator: w(x)=1x^0+139x^86+482x^87+325x^88+528x^89+410x^90+498x^91+316x^92+552x^93+323x^94+246x^95+131x^96+104x^97+4x^98+2x^99+8x^100+12x^101+2x^102+4x^105+2x^107+2x^108+1x^112+2x^115+2x^118 The gray image is a linear code over GF(2) with n=728, k=12 and d=344. This code was found by Heurico 1.16 in 0.953 seconds.