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 0 1 0 1 1 1 1 X^2+X 1 0 1 1 1 X^2+X 1 1 0 X^2+X 1 1 1 1 1 1 0 1 X^2+X 0 1 1 1 1 X 1 X^2+X 1 1 1 X^2+X 1 X^2+X 0 X^2 1 1 1 1 1 1 X X^2+X X^2 1 X^2+X 0 1 0 1 0 X 1 1 1 0 1 1 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 1 X^2+1 1 X+1 0 X^2+X X^2+1 1 X+1 1 0 X^2+X X^2+1 1 X^2 X+1 1 1 X+1 X^2+X X^2+X X+1 X^2+1 0 1 0 1 1 X^2+X 0 X^2+1 X 1 X^2+1 1 X^2+X X+1 1 1 X^2+1 1 1 1 X^2+X+1 X^2+1 X^2+X X^2+1 0 X^2+1 1 1 X X 1 1 X^2+1 1 1 1 X^2 X^2 X^2+1 X+1 X X+1 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 X^2 0 X^2 0 0 X^2 0 0 X^2 X^2 0 0 0 0 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 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 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 0 X^2 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 0 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 0 X^2 0 0 0 0 0 X^2 0 0 0 0 X^2 X^2 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 X^2 X^2 X^2 0 0 0 X^2 X^2 0 0 0 X^2 0 X^2 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 X^2 0 0 X^2 X^2 X^2 0 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 X^2 0 X^2 X^2 0 0 0 0 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 0 0 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 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 X^2 X^2 X^2 0 0 0 0 0 0 0 0 X^2 0 0 0 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 X^2 0 0 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 0 0 0 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 0 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 0 0 0 0 0 0 X^2 0 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 0 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 0 0 X^2 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 0 0 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 0 0 0 X^2 X^2 0 0 0 0 X^2 0 X^2 0 0 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 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 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 0 X^2 X^2 X^2 0 0 0 0 0 0 0 0 0 0 0 X^2 X^2 0 X^2 0 X^2 X^2 0 0 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 0 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 0 X^2 0 0 0 X^2 0 0 0 0 generates a code of length 82 over Z2[X]/(X^3) who´s minimum homogenous weight is 68. Homogenous weight enumerator: w(x)=1x^0+26x^68+12x^69+62x^70+48x^71+185x^72+172x^73+320x^74+418x^75+588x^76+780x^77+870x^78+1230x^79+1287x^80+1476x^81+1571x^82+1404x^83+1299x^84+1180x^85+905x^86+820x^87+534x^88+428x^89+261x^90+162x^91+122x^92+44x^93+53x^94+14x^95+34x^96+4x^97+37x^98+13x^100+13x^102+7x^104+3x^106+1x^110 The gray image is a linear code over GF(2) with n=328, k=14 and d=136. This code was found by Heurico 1.16 in 20.5 seconds.