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 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 X 1 1 0 1 X X 1 X^2 1 1 X 1 X 1 X^2 1 1 X^2 X 1 X 0 1 0 X 0 0 0 X X^2+X X X^2 0 X^2+X X^2 X X X 0 X^2+X X X^2+X X 0 0 X^2 0 X^2+X 0 X X^2 X X^2+X 0 0 X^2 X^2 X X^2+X X^2 X^2 X 0 X X^2 X^2 X 0 X X^2 X^2+X X X^2 X^2+X X^2+X X X^2+X X^2 0 X^2+X X 0 X^2 X^2+X X X^2 X^2+X 0 X^2 0 X^2+X X X X^2 X^2+X X^2+X X 0 X X 0 0 X^2 0 X 0 X X^2+X X^2+X 0 X 0 0 0 X 0 X X X 0 X^2 0 X^2+X X X^2 X^2+X X^2 X X^2 0 X^2+X X^2+X X^2 0 X X^2+X X^2 X^2+X X 0 0 X X 0 X^2 0 X^2+X X 0 X 0 X 0 X X^2+X X^2 X^2 X^2 0 0 X^2+X X^2+X X X 0 X X^2 X X^2 X X^2 X X^2+X X^2+X X X^2+X X^2 X^2+X X^2 0 0 X^2+X X^2+X X^2 X X^2 X^2 0 0 0 0 X^2 X X^2 X X^2 X^2+X X X X 0 0 0 0 X X 0 X X^2+X 0 X^2+X X X^2 X 0 X^2 X X 0 0 X X^2+X X^2 X^2+X 0 X^2+X 0 X X 0 X^2 X^2+X 0 X^2 X X^2 X X^2 X X^2 X^2 0 X^2+X X X^2 X^2+X X X^2+X X X^2+X 0 0 X^2 X^2+X X^2+X 0 X^2 X^2 X 0 X^2 X^2 X X X X X 0 X X^2 X^2 X X^2+X X X^2 X X 0 X X^2+X X^2+X X^2 X^2 0 X^2+X 0 X^2+X 0 X 0 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 0 X^2 0 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 0 X^2 0 0 0 0 0 0 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 0 0 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 0 0 0 0 0 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 0 0 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0 0 X^2 X^2 0 0 0 0 0 0 0 X^2 0 0 0 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+176x^82+4x^83+192x^84+64x^85+207x^86+104x^87+226x^88+164x^89+270x^90+132x^91+173x^92+24x^93+116x^94+16x^95+66x^96+4x^97+41x^98+34x^100+16x^102+7x^104+5x^106+4x^108+1x^110+1x^148 The gray image is a linear code over GF(2) with n=356, k=11 and d=164. This code was found by Heurico 1.16 in 80 seconds.