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 X 1 1 1 1 1 X 1 1 1 1 1 1 X^2 1 1 1 1 1 1 1 X 1 1 X 1 1 1 0 1 1 X 0 1 X^2 X X 1 1 0 1 X 1 1 1 1 X 0 X 0 0 0 X^2 0 X^2 0 X X X^2+X X X^2+X X^2+X X X^2 X X^2 0 0 X X X^2+X 0 X X X^2 0 X^2+X X^2+X X^2 X 0 X^2+X 0 0 X^2+X X X^2 X X 0 X^2 X X^2 0 X X^2+X X X^2+X X^2 0 X 0 X^2+X X^2 0 X^2 X^2 X 0 X^2 X^2+X 0 X^2+X X^2+X X^2+X 0 X^2 X^2 X^2 X^2+X X X^2 0 X X^2+X X^2 X 0 X^2+X X^2+X 0 X^2 X X^2+X X^2 X^2+X X^2+X X X 0 0 X X X^2 X 0 0 X 0 0 X^2 X X X X^2+X X X^2 X X^2+X 0 0 0 X X^2+X X^2+X X^2 0 X^2+X X^2 X^2+X X^2+X 0 X^2 X^2+X 0 X^2+X 0 X^2+X X^2 X^2+X X^2+X 0 0 X^2 X^2+X X^2+X X^2 X 0 X^2 0 X X X^2+X X^2 0 X^2+X 0 X^2+X 0 0 X^2 X X^2 X^2+X X^2 X^2+X X^2 X^2+X X 0 X X 0 X 0 0 X^2 X^2 X^2 0 0 X X^2+X X^2+X X^2 X^2 X^2+X X X^2 X^2 0 0 X X^2 X 0 X^2+X X X X X^2+X X 0 0 0 X 0 X X X^2+X X^2 0 X X 0 X^2+X X X^2 X^2+X X^2+X 0 0 X^2 X^2+X X^2 X X X^2+X 0 0 X 0 X^2 X^2+X X^2 X X^2+X X^2+X X^2 0 0 X X X X^2 0 X X X^2 0 0 X^2+X 0 X^2 X^2 X X^2+X X X^2 X X^2+X X^2+X X^2 X X 0 X X X^2+X X^2 X X^2+X 0 X^2 0 0 X^2 X^2 0 0 X X^2+X X^2 X^2+X X^2+X X^2 X^2+X 0 X^2 X^2+X X^2 X^2+X 0 X^2+X X^2+X X^2 X^2+X X^2 X X 0 0 0 0 X X X^2 X X^2+X X X 0 0 X^2 X X 0 X X^2+X 0 X^2+X X^2 0 X^2+X X^2 0 X^2 0 X^2+X X X^2+X X^2+X X^2 X^2+X X^2+X X X^2+X 0 X^2+X X^2 X^2 X X 0 0 X^2 X^2 X^2+X X^2 X X^2 X^2+X X 0 X^2+X 0 0 0 X^2+X X X^2+X 0 0 X 0 X^2 X^2 X X^2 X^2 X^2+X 0 X^2 0 X^2 X X^2+X 0 X 0 0 X X^2 X^2 X X^2+X X X^2 X^2 X^2+X X X^2+X X 0 0 X^2+X X^2+X X generates a code of length 98 over Z2[X]/(X^3) who´s minimum homogenous weight is 90. Homogenous weight enumerator: w(x)=1x^0+86x^90+166x^92+28x^93+206x^94+84x^95+268x^96+152x^97+220x^98+136x^99+194x^100+76x^101+162x^102+36x^103+85x^104+68x^106+32x^108+20x^110+17x^112+4x^114+4x^116+2x^122+1x^168 The gray image is a linear code over GF(2) with n=392, k=11 and d=180. This code was found by Heurico 1.16 in 1.02 seconds.