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 X 0 1 1 1 X 1 1 0 1 1 1 X 0 1 X 1 0 1 X 1 1 X 0 1 0 X 1 X X 1 X 1 0 X 0 X^2+X 0 X^2+X 0 X^2+X X^2 X^2+X 0 X^2+X 0 X^2+X X 0 0 X^2 X^2+X X^2+X X X^2+X X^2 X^2 X X X^2+X X 0 0 X^2 X^2 0 X^2+X X^2+X X 0 X^2 X^2 X^2+X X^2 X^2+X X X^2+X 0 X^2+X X^2+X X 0 X^2+X X^2+X X X^2+X X^2+X X X^2 X^2+X X X X X^2+X X^2+X X X 0 0 0 0 0 X^2 0 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 0 0 X^2 X^2 X^2 0 0 0 0 0 0 0 X^2 0 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 0 0 X^2 X^2 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 0 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 0 X^2 0 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 0 0 X^2 0 0 0 0 0 X^2 0 0 0 0 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 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 X^2 X^2 0 X^2 0 0 X^2 X^2 0 0 0 0 X^2 X^2 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 0 X^2 X^2 X^2 0 0 0 X^2 X^2 0 0 X^2 0 0 X^2 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 X^2 X^2 0 X^2 0 0 0 X^2 0 X^2 X^2 0 0 X^2 0 X^2 0 0 0 X^2 X^2 0 0 0 0 0 0 0 X^2 0 X^2 0 X^2 X^2 0 0 X^2 X^2 0 X^2 0 X^2 0 0 0 X^2 0 X^2 0 0 0 X^2 X^2 0 0 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 0 0 X^2 0 X^2 0 X^2 0 0 0 X^2 0 X^2 0 0 0 X^2 0 0 0 0 0 0 0 X^2 0 X^2 X^2 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 X^2 X^2 X^2 X^2 0 0 0 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 0 0 X^2 0 0 0 0 X^2 X^2 X^2 X^2 0 0 X^2 0 0 0 0 X^2 generates a code of length 67 over Z2[X]/(X^3) who´s minimum homogenous weight is 58. Homogenous weight enumerator: w(x)=1x^0+24x^58+32x^59+69x^60+60x^61+137x^62+118x^63+106x^64+190x^65+197x^66+230x^67+188x^68+182x^69+89x^70+114x^71+115x^72+74x^73+46x^74+18x^75+21x^76+6x^77+13x^78+9x^80+5x^82+2x^84+1x^88+1x^102 The gray image is a linear code over GF(2) with n=268, k=11 and d=116. This code was found by Heurico 1.16 in 0.535 seconds.