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 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 X 1 0 X 0 X^2+X X^2 X^3+X^2+X X^3+X^2 X X^2 X^2+X X^3 X^3+X 0 X^2+X X^2 X 0 X^2+X X^3+X^2 X^3+X X^3 X^3+X^2+X X^2 X X^3 X^3+X^2+X X^2 X X^2 X X^3 X^3+X^2+X 0 X^2+X 0 X^2+X X^2 X X^3+X^2 X^3+X 0 X^2+X 0 X^2+X X^2 X X^2 X X^3+X^2 X^3+X X^3+X^2 X^3+X X^2 X X^3+X^2 X^3+X 0 X^3 X^2+X X^3+X^2+X X^3 X^3+X^2+X 0 X^2+X 0 X^3 X^3 0 X^2+X X^3+X^2+X X^3+X^2+X X^2+X X^3 X^3 X^2+X X^3+X^2+X X^2+X X^3 X^3 X X^3+X X^3+X X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X X^3 X^2+X X^3 0 0 X^3+X^2 0 X^2 X^2 0 X^2 X^3+X^2 0 X^2 0 0 X^3+X^2 0 X^3+X^2 X^3 X^3 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 X^2 X^3+X^2 X^3+X^2 0 0 X^3+X^2 X^3+X^2 X^2 X^3+X^2 X^3 0 0 0 X^3+X^2 X^3+X^2 X^3+X^2 X^2 X^3 0 X^3+X^2 X^3 0 X^2 0 X^3 X^2 X^3+X^2 X^3 X^2 X^3 X^2 X^3 X^3 X^2 X^2 X^3 X^3 X^2 X^2 X^3 X^3 X^2 X^2 0 X^3+X^2 X^3 X^3 X^2 0 X^3+X^2 X^2 X^3+X^2 X^2 X^3 0 X^3+X^2 X^2 X^3 X^2 X^3 X^3 X^3 0 0 0 X^3 0 0 X^3 X^3 X^3 X^3 X^3 0 X^3 0 0 X^3 X^3 X^3 X^3 0 0 0 0 X^3 0 X^3 0 0 X^3 X^3 X^3 0 0 0 0 X^3 X^3 0 X^3 X^3 X^3 0 X^3 X^3 0 0 0 X^3 X^3 X^3 0 0 X^3 X^3 0 0 X^3 0 0 X^3 0 0 X^3 X^3 0 X^3 X^3 0 X^3 0 X^3 0 0 0 0 X^3 X^3 0 0 0 0 X^3 X^3 0 X^3 X^3 0 X^3 X^3 X^3 0 0 0 0 0 X^3 0 0 0 0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 0 0 X^3 0 X^3 X^3 0 0 X^3 X^3 0 0 X^3 X^3 0 X^3 0 X^3 0 X^3 0 X^3 0 0 X^3 0 X^3 0 X^3 0 X^3 X^3 X^3 0 0 X^3 0 0 X^3 0 X^3 X^3 0 X^3 0 0 X^3 X^3 X^3 0 0 X^3 X^3 X^3 X^3 X^3 0 0 0 0 0 X^3 0 0 X^3 0 X^3 0 X^3 X^3 0 0 X^3 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+27x^86+120x^87+70x^88+206x^89+233x^90+762x^91+212x^92+204x^93+65x^94+108x^95+21x^96+6x^97+10x^98+2x^99+1x^178 The gray image is a linear code over GF(2) with n=728, k=11 and d=344. This code was found by Heurico 1.16 in 1.33 seconds.