The generator matrix 1 0 1 1 1 X^2+X 1 1 0 1 1 X^2+X 1 X^2+X 1 1 1 0 1 X^2 1 X^2+X 1 1 X^2+X 1 1 0 1 1 1 X 1 1 1 0 1 X^2+X 1 1 1 0 1 1 0 1 0 1 1 1 1 0 X^2+X 1 0 0 1 1 X^2 X 1 1 1 1 1 1 1 1 1 1 1 1 1 0 X^2 1 0 1 1 1 1 1 1 0 0 1 X+1 X^2+X 1 1 0 X+1 1 X^2+X X^2+1 1 X^2+X 1 X+1 0 X^2+1 1 X^2 1 X^2+1 1 X^2+X X+1 1 X+1 X^2+X 1 X^2+1 0 X^2+1 1 X^2+X+1 0 X^2+X 1 X^2 1 X+1 0 X^2+1 1 X^2+X X^2+1 1 X+1 1 X^2+1 X^2+X X^2+1 X 1 1 0 1 1 X^2+X X^2+X+1 1 1 X^2+X X^2+1 X^2+1 X+1 X 1 0 0 X^2+X X+1 X^2+X+1 0 0 1 1 0 1 X X+1 X+1 X^2+X 0 X+1 1 0 0 X^2 0 0 0 0 0 0 0 0 0 0 0 X^2 0 X^2 X^2 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 X^2 X^2 0 0 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 0 X^2 0 X^2 0 X^2 0 X^2 0 0 X^2 0 0 X^2 0 0 X^2 0 0 X^2 X^2 0 0 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 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 X^2 0 0 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 0 0 0 X^2 0 0 X^2 0 X^2 0 0 0 0 X^2 0 X^2 X^2 X^2 0 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 X^2 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 X^2 0 0 X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 0 0 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 0 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 0 0 0 X^2 0 X^2 0 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 X^2 0 X^2 X^2 X^2 0 0 X^2 0 0 0 0 0 X^2 0 0 0 0 0 0 X^2 0 0 0 X^2 0 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 0 X^2 0 X^2 X^2 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 0 0 X^2 0 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 0 0 0 0 X^2 X^2 X^2 0 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 0 X^2 0 0 0 0 X^2 X^2 0 0 0 X^2 0 0 0 0 0 0 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 0 X^2 X^2 0 0 X^2 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 0 0 0 0 X^2 0 X^2 0 X^2 0 X^2 0 X^2 0 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 0 0 0 X^2 X^2 0 0 0 0 X^2 0 X^2 X^2 0 X^2 0 0 0 0 X^2 X^2 0 0 0 0 0 0 0 0 0 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 0 0 0 X^2 0 0 X^2 X^2 0 X^2 0 X^2 0 0 X^2 0 0 0 0 0 0 X^2 0 X^2 0 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 0 X^2 X^2 0 X^2 X^2 X^2 0 0 0 X^2 0 X^2 0 0 X^2 X^2 0 0 0 generates a code of length 84 over Z2[X]/(X^3) who´s minimum homogenous weight is 72. Homogenous weight enumerator: w(x)=1x^0+151x^72+20x^73+94x^74+152x^75+388x^76+504x^77+278x^78+1220x^79+557x^80+1736x^81+396x^82+2512x^83+471x^84+2512x^85+396x^86+1736x^87+494x^88+1220x^89+278x^90+504x^91+312x^92+152x^93+94x^94+20x^95+109x^96+36x^100+31x^104+8x^108+1x^112+1x^116 The gray image is a linear code over GF(2) with n=336, k=14 and d=144. This code was found by Heurico 1.16 in 22.5 seconds.