The generator matrix 1 0 1 1 1 0 1 X^2+X 1 1 1 X^2+X 1 1 X^2 X 1 1 1 1 1 1 1 X^2 1 1 X 1 1 0 1 X^2+X 1 1 X^2 1 X 1 1 X^2 1 X 1 1 0 1 X 1 1 1 1 1 X 1 1 1 1 1 1 1 X^2+X X X 1 X^2 1 1 1 0 X^2+X 1 X^2+X 0 X^2+X 1 1 X^2+X X^2 1 X^2+X 1 1 X 1 1 X^2 0 1 0 1 1 0 X^2+X+1 1 X 1 X^2+X+1 X^2 1 1 X X+1 1 1 X^2+X X^2+1 0 X+1 X X^2+1 0 1 X X^2+X+1 1 X X+1 1 X^2+X 1 0 1 1 X^2+1 1 0 X 1 X+1 1 X^2+X+1 X^2+1 1 1 1 X X^2+X X^2 0 X^2 X^2+X 0 X^2+X X^2+X X^2 X X X^2 1 1 X^2+X 1 1 1 0 0 1 1 X^2 1 X 1 X+1 X^2 1 1 X^2+1 1 X+1 X^2+X+1 1 X^2+X+1 X X 1 X^2+X+1 0 0 X 0 X^2+X X X^2 X^2+X 0 X X^2 0 X^2+X X^2 X X^2 0 X^2 X X X X X^2 X^2+X X^2+X 0 X^2 X^2 X X X^2+X X^2 X^2+X X^2+X X^2 X^2 X^2+X X^2 0 0 0 X X X^2+X X 0 0 0 X^2 X X^2+X X X^2 0 X^2 0 0 X^2+X X^2+X 0 0 X X X^2+X 0 X^2 X^2+X 0 X^2 X X^2+X X^2 X^2+X 0 X X^2 X^2+X 0 X^2 X^2+X X^2 X^2 X X^2 X X X^2 X 0 0 0 X 0 X X X X^2+X X^2 X^2+X X^2 0 X^2 X^2 X 0 0 X X^2+X X^2+X X X 0 X^2 X^2+X X 0 X^2 X^2+X X X^2 X^2+X X^2 0 X^2+X X^2+X X^2 X^2 X^2+X X^2 X^2 X X^2+X X^2 X^2 X^2+X X^2+X X X^2 0 0 X^2+X X X^2 X^2 X^2+X X^2 X^2+X 0 X^2+X 0 X X^2+X X^2 X X^2+X X^2 X^2+X X^2 X X^2 X^2 X X X^2 0 X 0 X^2 X^2+X X X^2+X X^2 X^2 X 0 X 0 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 0 0 X^2 0 X^2 X^2 0 0 0 X^2 0 0 X^2 X^2 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 0 X^2 0 X^2 0 0 0 0 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 0 0 0 X^2 0 X^2 0 X^2 X^2 0 0 X^2 0 0 X^2 X^2 0 0 X^2 X^2 X^2 0 0 X^2 0 0 0 X^2 generates a code of length 88 over Z2[X]/(X^3) who´s minimum homogenous weight is 82. Homogenous weight enumerator: w(x)=1x^0+160x^82+88x^83+296x^84+92x^85+288x^86+92x^87+247x^88+76x^89+160x^90+72x^91+141x^92+76x^93+128x^94+4x^95+65x^96+12x^97+28x^98+9x^100+2x^102+5x^104+2x^108+2x^110+1x^112+1x^120 The gray image is a linear code over GF(2) with n=352, k=11 and d=164. This code was found by Heurico 1.16 in 0.807 seconds.