The generator matrix 1 0 0 0 1 1 1 1 1 1 X^2 1 X^2+X 0 X^2 1 1 1 1 0 1 X^2+X 1 1 X^2+X X X^2+X 0 X^2+X 1 0 1 X^2 1 X^2 0 X 0 1 1 1 X^2+X X 1 1 1 0 X 1 1 X 1 0 X^2+X 1 X^2 1 1 X^2+X 0 0 1 0 X^2+X X^2 X^2+X 1 0 1 0 0 0 0 0 1 X+1 X^2+1 1 X^2+X+1 1 X 1 X^2+1 X^2+1 X^2+X X X^2+X X^2+1 1 X+1 X^2+X 1 X^2+X 1 1 X^2 0 X^2 X^2+X 1 1 1 0 X^2+X 1 1 0 X+1 1 1 X^2+X+1 X^2+X+1 X^2 1 1 1 X^2+X+1 1 0 1 1 X^2+X+1 X X X 1 1 1 X+1 X X^2 X 1 X+1 0 0 1 0 0 1 X^2+X+1 1 X X^2+X X+1 X+1 0 1 X^2+X+1 X^2 X+1 X^2+1 X^2 0 1 X^2 X^2+X X^2+X+1 X 1 X^2+1 X^2+X+1 1 X 1 X^2 0 X^2+X+1 1 1 X^2+X X^2+X X X+1 X^2+X X 0 0 1 X^2+X+1 X+1 X^2+X+1 0 X^2+X+1 X^2+X X+1 X^2 0 0 1 1 X^2 X^2+1 1 X^2+1 1 1 1 X^2+X 0 X+1 0 0 0 1 X+1 X^2+X+1 X^2+X X^2 X 1 1 X^2+1 X+1 X^2+X+1 X 1 0 0 1 1 X^2+1 1 X^2+1 X+1 X^2+X X^2+X+1 X^2+X X^2+X+1 X^2+X 1 X+1 X^2 1 X^2+X+1 X^2+1 X 1 X X^2+X+1 X+1 X^2 X^2+1 X X X+1 X+1 X^2+X+1 X X^2 X^2 X^2 X+1 X^2+1 X+1 X+1 X+1 X^2+X+1 X^2+X+1 X^2+X+1 X^2+X X^2+1 0 0 0 1 X+1 X^2 0 0 0 0 X^2 0 0 0 0 0 0 X^2 0 0 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 0 X^2 0 0 X^2 0 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 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 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 0 X^2 0 0 0 0 0 0 X^2 0 X^2 0 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 X^2 0 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 0 X^2 0 X^2 0 X^2 X^2 0 0 X^2 0 0 0 0 0 X^2 X^2 0 X^2 0 0 0 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+331x^58+520x^59+1041x^60+1208x^61+1800x^62+1844x^63+2545x^64+2612x^65+3019x^66+2984x^67+3048x^68+2640x^69+2620x^70+2000x^71+1677x^72+1000x^73+836x^74+432x^75+361x^76+88x^77+82x^78+28x^79+24x^80+4x^81+13x^82+6x^84+2x^86+1x^88+1x^90 The gray image is a linear code over GF(2) with n=268, k=15 and d=116. This code was found by Heurico 1.16 in 74.9 seconds.