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 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 X 1 1 0 X^2+X X^2 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 X 1 1 X^2 0 1 X^2+X 1 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 1 X^2+X+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 1 0 X^2+1 1 1 1 X X+1 X+1 X^2+1 1 1 X^2+X X^2+X 0 0 X^2+1 1 X X^2+X+1 X^2+X+1 1 1 X^2+1 X^2 1 X 1 1 0 1 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 0 X^2 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 0 X^2 0 0 0 X^2 0 X^2 0 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 0 0 X^2 0 X^2 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 0 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 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 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 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 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 0 X^2 0 0 0 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 0 0 X^2 0 0 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 0 0 0 0 X^2 0 X^2 X^2 0 X^2 0 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 0 X^2 0 X^2 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 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 0 X^2 0 X^2 X^2 0 X^2 0 X^2 0 0 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 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 0 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 0 0 0 0 X^2 0 0 0 0 X^2 X^2 0 X^2 X^2 X^2 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 X^2 0 X^2 0 0 X^2 0 X^2 0 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 0 X^2 0 0 generates a code of length 81 over Z2[X]/(X^3) who´s minimum homogenous weight is 70. Homogenous weight enumerator: w(x)=1x^0+26x^70+44x^71+76x^72+160x^73+193x^74+418x^75+353x^76+632x^77+409x^78+800x^79+500x^80+976x^81+553x^82+860x^83+403x^84+640x^85+280x^86+388x^87+156x^88+144x^89+42x^90+50x^91+17x^92+8x^93+17x^94+15x^96+9x^98+9x^100+4x^102+4x^104+3x^106+2x^108 The gray image is a linear code over GF(2) with n=324, k=13 and d=140. This code was found by Heurico 1.16 in 5.86 seconds.