The generator matrix 1 0 1 1 X^2 1 1 1 X^2+X 1 1 0 X^3+X 1 1 1 1 X^2 X^3+X^2+X 1 1 X^3 1 1 X^3+X X 1 1 1 1 X^3+X 1 X^3 1 1 1 X^2 1 1 X^3+X^2+X 1 1 X^3+X^2 X^3+X^2+X 1 X^3+X 1 0 X^3+X^2+X 1 X^3+X^2 1 0 X^3 X^3+X X^3+X^2+X X^3 1 X^3+X^2 X^3+X 0 X^2+X 1 X^3+X X^2 X^3 1 1 X^2 X^2+X 1 1 1 X 1 1 X^3 1 1 1 X 1 1 1 1 1 1 1 X^3 1 1 0 1 1 X^2+X 1 X^2+X+1 X^2 X^3+1 1 X+1 X^3+X^2+X 1 1 0 X^3+X^2+1 X^3 X^3+1 1 1 X^3+X X^2+X+1 1 X^3+X^2+X X^2+X+1 1 1 X^2 X^2+1 X^3+X^2 1 1 X^3+X 1 X^3+X+1 X^3+X+1 X^2+X 1 X^3+X X^2+1 1 X^3+X^2+X+1 X^3+1 1 1 X 1 0 1 1 X^2+X+1 1 X^2 X 1 1 1 1 0 X 1 1 1 X^3+X^2+X 1 1 1 X^2+1 X 1 1 X^3+X^2 X^3+1 X^2+X+1 X^3+X^2+X X^2+X X^3 0 X X^3+X+1 X^3 1 X^3+X+1 X^3+X^2 X^3+1 X^2+1 X^2+X X^3+X+1 X^3+X 1 X^3+X 0 0 0 X 0 X^3+X X X^3+X X^3 0 X^3 X^3+X X^3+X^2+X X^2 X^3+X^2 X^3+X^2 X^3+X^2+X X^3+X^2+X X^2+X X^3+X^2 X^3+X^2+X X^3+X^2+X X^3+X X^3+X^2 X^3+X^2 0 X X^2 X^2+X X^2+X X^2 X^3+X^2+X X^3 X^2 X^2 X^3+X X^2+X X^2+X X X^3+X X^3 0 X^3 0 X^2+X 0 X^3+X^2 X X^3+X^2+X X X^2+X X^3+X^2 0 X^3 0 X^3 X^3+X^2+X X^3+X X^3+X^2 X^3+X^2 X^3+X^2+X X^3+X^2 X^2 X^2 X X^2 X 0 X X^3 X^3+X X X^3+X^2 X^3+X X^2+X 0 X^3 X X^2+X X^2 X X^3+X X^2+X X^3+X^2 0 X^2 X^3+X^2+X X^3+X^2+X 0 X^3 X^3+X^2 X^3 0 0 0 X^3 0 X^3 X^3 X^3 X^3 0 0 X^3 X^3 0 X^3 X^3 0 0 0 0 X^3 X^3 X^3 0 0 0 X^3 X^3 0 0 X^3 0 X^3 X^3 0 X^3 X^3 X^3 X^3 0 X^3 0 X^3 0 X^3 0 0 0 X^3 0 0 0 X^3 X^3 X^3 X^3 0 X^3 X^3 0 X^3 X^3 0 X^3 0 0 0 0 X^3 0 0 X^3 0 X^3 0 X^3 X^3 X^3 0 X^3 X^3 X^3 0 0 0 X^3 X^3 0 X^3 0 X^3 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+32x^86+420x^87+492x^88+676x^89+385x^90+494x^91+286x^92+414x^93+344x^94+288x^95+95x^96+84x^97+8x^98+34x^99+13x^100+6x^101+1x^102+8x^103+4x^105+5x^106+4x^107+1x^116+1x^126 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 1.14 seconds.