The generator matrix 1 0 1 1 1 X^2+X 1 1 0 1 X 1 X^2 1 1 1 1 0 1 1 X^2+X 1 1 X^2+X 1 1 X^2 X^2 1 1 0 X^2+X 0 1 1 1 1 1 X^2+X X^2+X 1 1 1 1 1 X^2+X 0 X 1 1 1 1 0 X X^2 1 1 1 1 0 0 X 1 X X^2 X^2 1 1 1 X^2+X 1 1 X^2+X 1 1 1 1 0 X 0 1 1 X^2+X X^2+X+1 1 0 X+1 1 X 1 X^2+1 1 0 X^2+X+1 X^2 X^2+X+1 1 X^2+X 1 1 X^2+X 1 1 0 0 1 1 X+1 X+1 1 1 1 X^2+1 X^2+1 X^2 X^2+X+1 X+1 1 1 X^2 X X X^2 0 1 1 1 1 1 X^2+X 0 1 1 1 X^2+X 1 X^2+X+1 X+1 1 0 1 X X^2 X 1 X^2+X+1 X^2+1 X^2 1 X^2+X X^2+X 1 X X^2+1 X^2+X X+1 1 X 0 0 X 0 X^2+X 0 X^2+X 0 X^2+X X^2+X X X^2 X X^2 X X X^2 X^2 X X^2+X X^2 X^2 0 X^2+X 0 0 X X 0 0 0 0 X^2 X^2 0 X X X X^2 X^2 X X^2+X X X X X^2 X X X^2+X X X^2 X^2 0 0 X^2 X^2+X X^2+X X^2 0 X^2 X X^2+X X^2+X X^2+X X^2+X X^2+X X X X^2 X X^2+X X^2+X 0 X^2 X^2 X^2 0 X^2 X 0 0 0 X^2 0 0 0 0 0 0 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 0 0 X^2 X^2 0 X^2 0 X^2 0 0 X^2 0 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 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 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 0 0 X^2 X^2 0 0 0 0 X^2 0 0 0 0 X^2 X^2 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 0 0 X^2 0 X^2 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 0 0 0 X^2 X^2 0 X^2 X^2 X^2 0 0 0 0 0 X^2 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 0 0 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 0 0 0 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 0 0 X^2 X^2 0 0 0 0 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 0 0 0 0 0 0 0 0 0 0 X^2 0 0 X^2 0 0 0 0 0 X^2 0 0 X^2 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 X^2 0 X^2 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 X^2 X^2 X^2 0 0 0 0 0 X^2 0 X^2 0 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0 0 0 0 X^2 0 0 0 0 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 0 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 0 X^2 0 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 0 X^2 0 X^2 0 0 0 0 0 0 0 0 0 X^2 0 X^2 0 X^2 0 0 0 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 0 0 X^2 0 0 0 X^2 generates a code of length 79 over Z2[X]/(X^3) who´s minimum homogenous weight is 68. Homogenous weight enumerator: w(x)=1x^0+139x^68+16x^69+306x^70+160x^71+671x^72+492x^73+956x^74+772x^75+1484x^76+1008x^77+1562x^78+1200x^79+1702x^80+1096x^81+1488x^82+792x^83+945x^84+416x^85+442x^86+144x^87+317x^88+44x^89+96x^90+4x^91+80x^92+10x^94+27x^96+4x^98+6x^100+2x^104+2x^108 The gray image is a linear code over GF(2) with n=316, k=14 and d=136. This code was found by Heurico 1.16 in 19.9 seconds.