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 1 0 1 1 1 0 1 X^2 1 1 X^2+X 1 1 1 X^2+X 1 1 0 1 0 1 X^2+X 1 1 1 0 X^2 1 1 1 1 1 1 1 1 X^2+X 1 0 1 X^2+X 1 1 1 X^2 1 1 1 0 1 X^2 1 1 1 1 X^2+X 1 1 1 1 X^2+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 1 X^2+X+1 0 X 1 X^2+1 X^2+1 X^2+X 1 X+1 1 0 X^2+X 1 X^2 X+1 X^2+1 1 X+1 X^2+1 1 0 1 X^2+X 1 X+1 0 X 1 1 0 X^2+1 X^2 0 X+1 X^2+X X^2+X+1 0 1 X^2+X+1 1 X^2+X 1 X^2+1 0 X+1 1 X^2+1 X X^2+1 1 X^2+X 1 X^2+X X^2+X X 1 1 X^2+1 X^2 X 1 1 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 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 0 0 X^2 X^2 X^2 0 0 X^2 X^2 0 0 0 0 X^2 X^2 0 0 0 X^2 X^2 X^2 0 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 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 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 X^2 X^2 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 0 X^2 0 X^2 X^2 0 0 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 0 0 0 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 X^2 0 0 X^2 0 0 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 0 0 0 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 0 0 0 0 0 X^2 X^2 0 0 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 0 X^2 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 0 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 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 0 0 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 0 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 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 0 X^2 0 0 0 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 0 0 0 0 X^2 0 X^2 X^2 0 0 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 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 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 0 0 X^2 0 0 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 0 X^2 0 X^2 0 0 X^2 X^2 0 0 X^2 0 0 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 0 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 0 X^2 0 0 0 X^2 0 X^2 X^2 X^2 0 0 0 0 0 0 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 0 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 generates a code of length 83 over Z2[X]/(X^3) who´s minimum homogenous weight is 72. Homogenous weight enumerator: w(x)=1x^0+50x^72+22x^73+121x^74+168x^75+264x^76+310x^77+381x^78+528x^79+569x^80+692x^81+708x^82+656x^83+696x^84+692x^85+556x^86+528x^87+345x^88+310x^89+209x^90+168x^91+101x^92+22x^93+36x^94+14x^96+20x^98+2x^100+8x^102+5x^104+4x^106+1x^108+3x^110+2x^114 The gray image is a linear code over GF(2) with n=332, k=13 and d=144. This code was found by Heurico 1.16 in 6 seconds.