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 0 1 1 1 X^2 1 X^2 1 1 1 1 1 X 1 1 1 X 1 1 1 X^2 1 1 0 1 X^2 1 1 1 1 X 1 X 1 X^2 1 1 X 1 1 X 1 1 1 0 X 0 0 0 0 0 X^2 X^2 X X^2+X X X X X^2+X X 0 X^2+X X^2 X X^2 X 0 X X^2 X^2+X X 0 X^2+X X^2 X^2+X 0 0 X^2 0 X X X^2+X X^2 X^2 X^2+X 0 0 X^2+X X^2 X^2 0 X X X X X X^2 0 0 X^2+X X 0 0 X X^2+X X^2+X X^2 0 0 X^2+X X^2+X X X^2 X 0 X^2 X^2+X 0 X^2+X X^2 X 0 0 X^2 X^2 X^2 X^2+X X^2+X X^2 X^2+X 0 X^2 0 0 X 0 0 X^2 X^2+X X X X X X X^2+X 0 0 0 X^2 X^2 X^2+X X X^2 0 0 X^2+X X^2 X^2 X X^2+X 0 X X X^2+X X X^2+X X^2+X 0 X^2 0 0 X^2 X^2+X X^2 X X X X^2 0 X X X^2+X 0 0 0 X^2+X 0 X^2 X^2+X X^2 0 0 X X^2+X X X^2 0 X^2 0 X^2 0 X X^2 0 X^2 X^2+X X^2 X^2 X^2+X X^2+X X^2 X^2+X X X^2 0 X X X X^2 X^2 0 0 0 X 0 X^2+X X^2+X X X^2 X^2+X X^2+X 0 0 X X X^2 X X^2 X^2+X 0 X^2+X 0 X^2 X X^2 X X X^2 X X 0 0 X^2 X 0 X^2+X X^2 X^2+X X X^2 0 0 X X^2+X 0 X^2+X X^2+X 0 X^2+X X^2+X 0 X^2+X X^2 X^2 0 X^2+X 0 X X^2 X^2 0 X^2 X X^2+X X X 0 X X 0 X^2 X^2 X^2+X X X^2 X^2+X X^2+X X X X^2+X X^2+X X X 0 0 X 0 0 0 0 0 0 X X X^2 X^2+X X X^2+X X^2 X^2 X X^2 X^2+X X X X^2 X^2 X^2+X 0 X^2+X 0 X^2+X X^2+X X^2+X 0 X^2+X 0 X 0 X^2 0 X^2+X X 0 X^2 X^2+X X^2+X 0 X^2+X X^2+X 0 X^2+X X^2 X^2+X X^2 0 X^2+X X^2 X X^2 0 0 X^2+X X^2+X 0 X^2 X^2 X^2 X X^2 X^2 X^2+X X^2+X 0 X X^2+X 0 X^2+X 0 X 0 0 X^2 X X^2+X X^2 X^2+X 0 X 0 X X^2+X X^2+X X^2+X 0 X^2 generates a code of length 88 over Z2[X]/(X^3) who´s minimum homogenous weight is 80. Homogenous weight enumerator: w(x)=1x^0+43x^80+68x^81+90x^82+118x^83+148x^84+126x^85+143x^86+222x^87+222x^88+232x^89+167x^90+102x^91+76x^92+72x^93+52x^94+38x^95+31x^96+20x^97+23x^98+14x^99+20x^100+10x^101+2x^102+1x^104+2x^106+2x^107+2x^108+1x^150 The gray image is a linear code over GF(2) with n=352, k=11 and d=160. This code was found by Heurico 1.16 in 0.776 seconds.