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 1 X 1 0 1 1 1 X^2 1 X^2+X 1 1 1 0 1 X^2+X 1 1 X^2+X 0 1 1 1 1 1 X^2+X 1 0 1 0 1 1 X^2 1 1 X^2+X 0 X 1 1 1 1 X 0 1 X^2 1 1 X^2 1 1 1 1 0 X^2 1 1 0 X 0 1 0 1 X+1 X^2+X 1 1 0 X+1 1 X^2+X X^2+1 1 1 0 X^2+1 1 X^2+X X+1 X^2+X+1 1 0 1 X^2+X X^2+1 X^2+1 1 0 1 X^2+X X+1 X^2 1 X^2+1 1 X^2+X X+1 1 1 X+1 0 X^2+X X+1 0 1 X^2+X 1 X+1 1 X^2+1 X^2+1 1 X 0 1 1 1 X+1 X^2+X+1 X X^2 1 1 X^2+1 1 0 0 1 X^2+X X+1 X+1 0 X 1 X^2+X+1 X^2+X+1 1 X 1 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0 X^2 X^2 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 0 X^2 X^2 0 X^2 0 0 0 X^2 0 0 0 0 X^2 X^2 0 X^2 X^2 0 0 X^2 0 0 0 X^2 X^2 0 X^2 0 X^2 0 0 X^2 0 0 X^2 X^2 X^2 X^2 0 0 X^2 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 0 X^2 0 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 0 0 0 0 X^2 0 0 0 0 0 X^2 X^2 X^2 X^2 0 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 X^2 X^2 0 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 0 0 X^2 0 0 X^2 0 X^2 0 X^2 X^2 0 X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 X^2 X^2 X^2 0 0 0 0 0 0 X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 0 0 X^2 X^2 0 X^2 0 0 X^2 0 0 0 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 0 0 X^2 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 0 X^2 0 X^2 0 0 X^2 0 0 0 0 0 0 0 0 X^2 0 0 X^2 X^2 0 0 X^2 X^2 0 0 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 0 0 X^2 0 0 0 0 0 X^2 0 0 X^2 0 X^2 0 0 X^2 0 0 X^2 0 X^2 0 X^2 0 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 0 0 0 0 0 0 0 0 0 X^2 0 X^2 0 0 0 0 0 0 X^2 X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 0 0 0 X^2 X^2 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 0 0 0 0 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 0 0 0 0 X^2 0 0 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 0 X^2 X^2 0 0 X^2 0 X^2 0 X^2 0 X^2 0 X^2 0 X^2 X^2 0 0 X^2 0 0 0 0 0 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+48x^68+46x^69+64x^70+194x^71+138x^72+452x^73+208x^74+786x^75+282x^76+1040x^77+328x^78+1128x^79+319x^80+1052x^81+254x^82+760x^83+173x^84+418x^85+101x^86+198x^87+42x^88+64x^89+37x^90+6x^91+8x^92+14x^94+10x^96+12x^98+1x^100+5x^102+2x^104+1x^106 The gray image is a linear code over GF(2) with n=316, k=13 and d=136. This code was found by Heurico 1.16 in 5.37 seconds.