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 1 1 1 1 1 1 1 0 X 1 X 1 X^2 1 X 0 1 0 X 0 1 0 X^2 X 1 1 0 X X 0 X 1 1 X X 1 0 1 X^2 1 1 1 1 X^2 X 0 0 0 1 X 1 0 X 0 0 0 X X^2+X X 0 X^2 X^2 X X^2+X 0 X^2+X X X^2 X^2+X X^2+X 0 0 X X^2+X X^2+X 0 0 X^2+X X X^2 0 0 X X X X 0 0 X X^2 X X X X^2 X^2+X X X X^2 0 X^2 X X^2+X X^2 X^2 0 X X^2+X 0 X^2+X X 0 X 0 X^2 0 X^2+X X^2 0 X^2 0 X X^2 X^2+X X^2 X^2+X 0 X X 0 0 X X^2 0 0 0 0 X 0 X X X^2+X 0 0 0 X X^2 X X^2+X X^2 X^2+X X^2 X^2 X^2 0 X X X^2+X X^2 X^2 X X X^2 X X^2+X 0 X X^2+X X^2+X X^2+X 0 X X^2+X X X^2 X X^2+X 0 X^2+X 0 X^2+X X X^2 0 X^2 X^2+X X^2 X X X^2+X X^2 X^2+X X^2 X X X X X^2 X^2 X X^2 X^2+X X^2 X X^2 X 0 X^2+X X^2+X 0 X^2 0 X 0 X 0 X^2+X 0 0 0 0 X X 0 X^2+X X 0 X 0 X X^2+X X^2+X X^2 X^2 0 X^2 X X^2+X 0 0 X^2+X X^2+X X 0 X 0 X X 0 0 X^2 X^2 X X^2 X^2 0 X 0 X^2 X X X^2 X X 0 X X^2+X 0 X X 0 X^2 0 X^2 0 0 X^2+X X 0 X^2+X X^2+X X^2 X X X X^2+X X^2+X X X 0 X X^2 X^2 X^2 X^2+X 0 X X 0 X^2 0 0 0 0 0 X^2 0 0 0 0 X^2 X^2 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 0 0 X^2 X^2 0 X^2 X^2 0 0 0 X^2 0 0 X^2 X^2 0 0 X^2 0 X^2 X^2 0 0 0 0 X^2 0 0 0 0 0 0 X^2 0 0 0 X^2 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 X^2 X^2 0 0 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 0 0 0 X^2 0 0 X^2 X^2 0 X^2 0 0 X^2 0 0 X^2 X^2 X^2 X^2 0 0 0 0 0 X^2 0 X^2 X^2 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 0 0 X^2 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0 0 0 0 0 0 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 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 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 0 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 0 0 0 0 0 0 0 X^2 0 0 0 0 X^2 X^2 0 0 X^2 X^2 0 X^2 0 0 0 X^2 X^2 0 X^2 X^2 X^2 0 0 0 X^2 0 0 0 X^2 X^2 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 0 0 0 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 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 0 0 X^2 0 0 X^2 0 0 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 0 X^2 X^2 0 0 0 X^2 X^2 0 0 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 0 0 0 X^2 0 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 generates a code of length 83 over Z2[X]/(X^3) who´s minimum homogenous weight is 70. Homogenous weight enumerator: w(x)=1x^0+39x^70+118x^71+190x^72+246x^73+322x^74+388x^75+513x^76+636x^77+732x^78+908x^79+1031x^80+1148x^81+1354x^82+1220x^83+1220x^84+1260x^85+1033x^86+1006x^87+793x^88+558x^89+424x^90+348x^91+250x^92+196x^93+150x^94+96x^95+69x^96+48x^97+30x^98+12x^99+24x^100+4x^101+6x^102+3x^104+6x^106+1x^108+1x^112 The gray image is a linear code over GF(2) with n=332, k=14 and d=140. This code was found by Heurico 1.16 in 28.6 seconds.