The generator matrix 1 0 1 1 1 0 1 X^2+X 1 X^2 1 1 1 1 0 1 1 1 1 0 1 0 1 X^2 1 1 X X^2+X 1 1 1 X^2 1 1 1 X^2+X 1 X 1 X^2 1 X^2 1 1 X^2 1 1 X 1 1 X 1 1 1 X^2 X X 1 0 1 X^2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X^2+X 1 1 1 X^2+X X^2 X 1 1 X^2 1 1 1 1 0 1 1 0 X^2+X+1 1 X 1 X+1 1 X^2+X X^2+1 X^2 1 1 X^2+X+1 X 1 X 1 X^2 1 X^2+1 1 X^2 X^2+X+1 1 1 X+1 X^2+X 0 1 0 X X^2+X+1 1 X^2+1 1 X^2+1 1 X^2+X+1 1 1 X^2 1 1 0 1 0 X^2 1 X X^2+X X^2+X 1 1 1 X^2 1 X^2+1 X X^2+X 1 X^2+X+1 1 X^2+X+1 1 0 0 1 X+1 1 X^2+X+1 X^2+X+1 X+1 1 X^2 0 X^2 1 1 1 X X^2+X+1 1 X^2 X^2+1 X 0 0 0 X 0 X^2+X X X^2 X X^2+X X 0 X^2+X X^2+X 0 X^2 0 X^2+X X^2 X 0 X X X^2 X^2+X X^2 X 0 X X^2 0 X^2 X^2 X^2+X X^2+X X^2 X^2+X X^2+X X^2+X X X X^2+X X^2 X^2 X 0 0 X^2+X 0 0 0 X^2+X X X^2 X^2+X X^2+X 0 X X 0 0 X^2+X X^2+X X^2+X X X 0 X^2 X^2 X^2 X X 0 X^2+X 0 0 X^2 X X^2+X X^2+X 0 X^2+X X^2 X^2+X X X^2+X X^2 X^2 X^2 X 0 0 0 X 0 X X X X X^2 X^2 X^2+X X^2 X^2+X X X^2+X X^2 X^2 X^2+X 0 X^2+X X^2 X^2 X^2+X X^2+X X^2 X X^2 X^2 X^2 0 X^2+X X^2 X^2 X^2 X^2 X^2+X X X^2 X X X^2+X X X^2+X X^2 X^2+X X X^2 0 X X X X^2+X X 0 X^2+X X^2 X^2 X X^2 X X^2 X X 0 X^2+X X^2+X X X^2 X^2+X X^2 X^2 X^2 X 0 X^2 X X^2+X 0 0 X^2+X X X^2+X X^2+X X X^2+X 0 X 0 0 0 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 0 0 X^2 X^2 X^2 X^2 0 0 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 0 X^2 X^2 0 0 0 0 X^2 X^2 0 0 0 X^2 X^2 X^2 0 0 0 X^2 X^2 0 0 X^2 X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 0 X^2 0 X^2 X^2 0 0 0 0 X^2 X^2 0 0 X^2 0 0 0 generates a code of length 89 over Z2[X]/(X^3) who´s minimum homogenous weight is 83. Homogenous weight enumerator: w(x)=1x^0+144x^83+166x^84+232x^85+102x^86+200x^87+165x^88+194x^89+91x^90+176x^91+105x^92+170x^93+84x^94+116x^95+32x^96+36x^97+1x^98+2x^99+4x^100+2x^101+6x^102+6x^104+6x^105+2x^106+2x^107+1x^114+1x^116+1x^122 The gray image is a linear code over GF(2) with n=356, k=11 and d=166. This code was found by Heurico 1.16 in 9.07 seconds.