The generator matrix 1 0 1 1 1 X^2+X 1 1 0 1 1 X^2+X 1 X^2+X 1 1 0 1 1 1 0 1 X^2+X 1 1 0 1 1 X^2+X 1 1 1 1 0 1 X^2+X 1 1 1 1 0 X^2+X 1 1 0 X 1 1 1 1 X^2+X 1 X^2 X^2+X 1 1 1 1 X 0 1 1 1 1 1 1 X 1 1 X^2 1 X 1 X^2+X 1 X^2+X 1 0 X 1 1 0 1 X+1 X^2+X 1 1 0 X+1 1 X^2+X X^2+1 1 X^2+X 1 X+1 0 1 X^2+1 0 X^2+1 1 X^2+X 1 X+1 X^2+X+1 1 X^2+X X^2+1 1 0 0 X+1 X^2+X 1 X^2+1 1 0 X^2+X X X^2+1 1 1 X^2+1 X+1 1 1 0 X+1 0 X^2+1 1 X^2+X 1 1 X^2+1 X^2+1 X^2 X^2+1 1 1 X^2 1 X+1 X^2+X X^2+X X^2+1 1 X^2+X X+1 1 X^2+1 0 0 1 X^2+X+1 1 1 1 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 0 X^2 0 X^2 0 X^2 0 X^2 0 0 0 X^2 X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 0 0 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 0 0 0 X^2 0 0 0 0 0 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 0 0 0 0 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 0 0 0 X^2 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 0 0 0 0 0 0 0 X^2 0 0 0 0 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 0 X^2 X^2 0 X^2 X^2 0 X^2 0 0 X^2 X^2 0 0 X^2 0 X^2 0 X^2 X^2 0 X^2 0 0 X^2 0 0 X^2 X^2 X^2 0 0 X^2 0 0 X^2 X^2 0 X^2 X^2 0 0 X^2 0 0 X^2 0 X^2 0 0 X^2 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 0 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 0 0 0 0 X^2 0 0 X^2 X^2 0 X^2 0 0 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 X^2 X^2 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 0 0 0 X^2 0 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 0 0 X^2 X^2 0 X^2 0 0 0 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 0 0 0 0 0 0 0 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 0 0 X^2 X^2 0 X^2 0 0 0 X^2 0 0 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 0 X^2 0 0 X^2 X^2 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 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 0 0 0 0 X^2 X^2 0 X^2 0 X^2 X^2 0 0 X^2 0 0 0 X^2 0 X^2 X^2 X^2 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 0 X^2 0 0 X^2 X^2 0 X^2 0 X^2 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 0 0 0 X^2 0 generates a code of length 81 over Z2[X]/(X^3) who´s minimum homogenous weight is 68. Homogenous weight enumerator: w(x)=1x^0+35x^68+10x^69+109x^70+128x^71+148x^72+438x^73+235x^74+758x^75+369x^76+1522x^77+521x^78+2080x^79+677x^80+2388x^81+667x^82+2164x^83+510x^84+1414x^85+351x^86+872x^87+201x^88+358x^89+91x^90+134x^91+54x^92+14x^93+43x^94+8x^95+42x^96+13x^98+7x^100+16x^102+3x^104+2x^106+1x^108 The gray image is a linear code over GF(2) with n=324, k=14 and d=136. This code was found by Heurico 1.16 in 21.4 seconds.