The generator matrix 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X 0 0 0 X X^2 X 1 X 1 1 0 1 1 1 X 1 0 1 1 X X 0 X^2 1 1 X^2 X 0 0 X^2 1 1 X 1 1 X 1 1 X 0 1 1 1 1 0 X 0 X 0 0 X X^2+X 0 0 X X^2+X X^2 0 X^2+X X^2+X X^2 X^2 X X X X^2+X X 0 X^2 0 X^2+X 0 0 X X^2 X X^2 X^2+X X^2 0 X X^2+X X X X^2+X X^2 X X^2 0 X^2 0 X X^2 X^2 X X X 0 X^2 X X X^2+X 0 X X X X X X^2+X X X X 0 X^2+X X^2+X 0 0 X 0 0 X^2 0 0 0 X X 0 X^2+X X 0 0 X^2+X X 0 X X^2 X 0 X^2 X X X^2 X^2+X 0 X 0 X^2+X X^2 X^2 X^2+X X^2+X 0 X^2 0 X X^2 X X X^2 0 X X 0 X X^2 X^2+X X 0 X X X X^2 X^2 X^2 X X^2+X X X X^2+X X^2+X X^2+X X^2+X X^2 X^2 X^2+X 0 X X^2+X X^2+X X^2+X X X^2 X 0 X X^2 X X^2 X 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 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 0 X^2 X^2 X^2 X^2 0 0 0 0 X^2 X^2 0 X^2 0 X^2 0 X^2 0 0 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 X^2 0 0 0 0 0 0 X^2 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 0 0 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 0 0 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 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 X^2 X^2 X^2 0 0 0 0 0 0 X^2 0 0 0 0 0 0 X^2 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 0 X^2 X^2 0 X^2 0 X^2 0 0 X^2 0 0 X^2 X^2 0 X^2 0 0 0 0 X^2 0 X^2 0 0 X^2 0 X^2 X^2 X^2 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 0 0 0 0 0 0 X^2 0 0 0 X^2 0 0 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 0 X^2 X^2 0 X^2 0 0 X^2 X^2 0 X^2 X^2 0 0 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 0 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 0 0 X^2 X^2 0 0 X^2 0 0 0 0 0 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 0 0 0 0 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 0 X^2 X^2 0 X^2 0 0 X^2 0 0 X^2 0 0 0 X^2 0 0 0 X^2 0 0 X^2 X^2 0 X^2 X^2 0 0 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 0 0 X^2 X^2 0 0 0 0 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 0 0 X^2 0 0 0 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 0 0 X^2 X^2 0 0 0 0 0 0 0 0 0 0 X^2 0 X^2 0 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 0 0 0 0 0 0 X^2 0 X^2 0 0 0 0 0 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 0 X^2 X^2 0 X^2 0 X^2 0 0 0 0 generates a code of length 78 over Z2[X]/(X^3) who´s minimum homogenous weight is 64. Homogenous weight enumerator: w(x)=1x^0+31x^64+20x^65+143x^66+126x^67+210x^68+296x^69+280x^70+620x^71+380x^72+1020x^73+405x^74+1786x^75+414x^76+2304x^77+445x^78+2194x^79+415x^80+1830x^81+386x^82+1138x^83+374x^84+536x^85+225x^86+240x^87+151x^88+120x^89+114x^90+38x^91+50x^92+16x^93+39x^94+2x^95+13x^96+2x^97+7x^98+8x^100+3x^102+1x^104+1x^106 The gray image is a linear code over GF(2) with n=312, k=14 and d=128. This code was found by Heurico 1.16 in 26.8 seconds.