The generator matrix 1 0 1 1 1 X^2+X 1 1 X^2 1 X 1 1 X^2 1 X^2 1 1 X^2+X 1 1 1 1 X^2+X 1 1 1 1 X^2 X^2+X 1 X 1 1 0 X^2 X^2 1 1 1 1 1 1 0 1 1 0 1 1 X^2 1 1 X^2+X X^2+X 1 1 1 0 X^2 1 X^2+X 1 1 1 0 1 0 1 1 X^2 X 1 1 1 1 1 X^2 X^2 0 0 1 1 0 1 1 X X^2+X+1 1 1 1 X^2+X X+1 1 X^2 1 1 X^2+X 1 0 X+1 X^2+X X+1 1 X+1 X^2 1 X 1 1 X^2+X+1 1 0 X^2+X+1 1 1 1 X^2 X^2+1 X^2 0 X^2+X+1 1 1 X^2+X+1 0 1 0 X+1 1 X^2 X^2+X+1 1 1 X^2+X X^2+X+1 0 1 1 X^2+1 1 X X^2+X X^2 0 1 1 X X^2+X+1 X^2 0 X+1 X X X+1 X+1 1 1 1 0 0 X 0 0 0 0 0 0 X^2 X^2 0 0 X X^2+X X^2+X X X X X X^2+X X X X X^2 X^2 X X X^2 0 X X 0 X^2+X X^2 X^2+X X^2 X X^2 X^2 X^2 X^2+X 0 X^2 X^2+X X^2+X X^2+X X^2 X^2 X 0 X X^2+X X^2+X 0 X^2+X X^2+X X 0 0 0 X 0 X X^2 X^2+X X^2 0 X X 0 X 0 X X^2+X 0 X^2 0 0 0 0 0 X 0 0 X X X X^2+X X X^2 0 X^2 0 X X X X^2 X 0 0 X^2+X X^2+X 0 X^2 X^2 0 X^2 X X X^2+X X^2+X 0 X^2+X X^2+X X^2 X^2+X X^2+X 0 X X X^2+X X^2+X X^2 X^2 X^2 X^2 0 X^2 X^2+X X^2 X^2+X 0 X X^2+X X^2 0 0 0 X^2 X^2+X 0 X^2+X 0 X X^2+X X^2 X^2 X^2+X X X^2+X X X X X X X^2 X^2+X 0 0 0 0 X 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2+X X^2+X X^2+X X^2+X X^2+X X^2+X X^2+X X^2+X X X^2+X X X X^2+X X X X X^2+X X X^2 0 0 X 0 X X X^2+X X^2 X^2 X X^2 X^2 X^2+X X X^2+X X^2+X X^2 X^2 0 X^2+X X X^2+X X^2 X X^2+X X^2+X 0 X X X X 0 X X^2+X X^2+X 0 0 0 0 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 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 X^2 X^2 0 0 X^2 0 0 0 0 X^2 0 X^2 X^2 0 0 0 X^2 0 X^2 0 0 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 generates a code of length 79 over Z2[X]/(X^3) who´s minimum homogenous weight is 70. Homogenous weight enumerator: w(x)=1x^0+64x^70+156x^71+301x^72+400x^73+441x^74+514x^75+648x^76+680x^77+640x^78+716x^79+649x^80+644x^81+614x^82+478x^83+391x^84+270x^85+176x^86+152x^87+89x^88+42x^89+39x^90+22x^91+24x^92+10x^93+6x^94+8x^95+8x^96+2x^97+2x^98+2x^99+1x^100+2x^102 The gray image is a linear code over GF(2) with n=316, k=13 and d=140. This code was found by Heurico 1.16 in 5.74 seconds.