The generator matrix 1 0 1 1 1 X^2+X 1 1 0 1 1 X^2+X 0 1 1 X^2+X 1 1 X 1 1 1 1 0 1 1 0 X^2+X 1 1 1 1 0 1 X^2+X 1 0 1 X^2 1 1 X^2+X 1 1 1 X^2+X 1 X^2+X 1 1 0 1 1 1 X^2+X 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 X^2 1 1 X 1 1 1 1 X^2 1 1 0 1 X 0 1 X+1 X^2+X 1 1 0 X+1 1 X^2+X X^2+1 1 1 X^2+X X+1 1 X^2+1 0 1 X^2 X+1 X^2+X+1 X^2+X 1 X^2+1 0 1 1 X^2+X X^2+1 X^2+X X^2+1 1 X+1 1 0 1 0 1 X^2+1 X^2+X 1 X+1 X^2 X^2+X+1 1 1 1 X^2+X 0 1 X^2+1 0 X+1 1 0 0 X^2+X+1 1 1 1 X^2+1 X 1 X X+1 X+1 X+1 X^2+X X^2 X^2+X 1 1 1 X^2+X 1 X^2+1 0 X X+1 1 0 X 1 X^2+X X^2+X 0 0 X^2 0 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 0 0 0 X^2 0 X^2 X^2 0 0 0 0 X^2 X^2 X^2 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 0 X^2 0 X^2 0 0 X^2 X^2 0 X^2 0 X^2 0 X^2 0 0 0 X^2 0 0 0 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 0 X^2 0 X^2 0 X^2 0 X^2 0 0 0 0 X^2 0 X^2 X^2 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 0 X^2 X^2 0 0 X^2 X^2 0 0 0 X^2 0 X^2 0 0 0 X^2 0 0 0 0 X^2 0 0 0 0 0 0 X^2 X^2 0 0 X^2 X^2 0 0 0 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 0 0 X^2 0 0 X^2 X^2 0 0 0 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 0 0 0 X^2 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 0 X^2 0 0 0 0 0 0 0 X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 0 X^2 0 0 0 0 X^2 0 X^2 0 0 0 X^2 0 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 0 X^2 0 0 0 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 0 0 0 X^2 0 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 0 0 X^2 X^2 0 0 X^2 X^2 0 X^2 0 0 X^2 0 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 0 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 0 X^2 X^2 0 0 X^2 X^2 0 0 X^2 X^2 0 0 0 0 X^2 X^2 X^2 0 0 X^2 0 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 0 X^2 0 0 0 0 0 0 0 X^2 0 X^2 0 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 0 0 0 0 0 X^2 0 X^2 0 X^2 0 0 0 0 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 0 0 X^2 0 X^2 X^2 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 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 0 0 0 0 0 X^2 0 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 0 0 X^2 X^2 0 X^2 0 0 X^2 X^2 0 0 0 0 X^2 0 0 X^2 X^2 0 0 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 0 X^2 0 0 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 0 0 0 X^2 0 X^2 0 X^2 0 X^2 0 X^2 generates a code of length 86 over Z2[X]/(X^3) who´s minimum homogenous weight is 76. Homogenous weight enumerator: w(x)=1x^0+145x^76+20x^77+202x^78+124x^79+548x^80+328x^81+538x^82+504x^83+749x^84+560x^85+784x^86+560x^87+793x^88+504x^89+560x^90+328x^91+441x^92+124x^93+214x^94+20x^95+87x^96+6x^98+15x^100+22x^104+10x^108+4x^112+1x^120 The gray image is a linear code over GF(2) with n=344, k=13 and d=152. This code was found by Heurico 1.16 in 6.49 seconds.