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 X 0 X^2 X^2 X X 0 1 1 X^2 0 1 X 1 X 0 1 1 X^2 X^2 1 X 1 1 X 1 X^2 X X^2 0 1 1 1 1 0 X 0 0 0 0 0 0 0 X^2+X X X X X X^2 X^2+X 0 X X 0 X^2 X^2 X^2+X X^2 X X^2+X 0 X X^2 0 X^2 0 0 X^2+X X 0 X^2+X X^2+X X X^2 X X^2+X X X X^2 X^2+X X X X^2+X X X X^2+X X X^2+X X X X^2 0 0 X 0 0 X^2+X X^2 X^2 X X^2 0 X^2+X X X^2+X 0 0 X 0 0 0 X X^2+X X X^2 X X^2+X 0 0 X X X^2 X^2+X X^2+X X^2+X 0 X^2+X X^2+X X^2+X X^2+X X^2 X^2 X^2+X X^2+X X^2 0 X^2 X^2 X^2+X 0 X^2 X^2 X^2 0 X 0 X^2+X X^2+X X^2 X 0 X^2+X X^2 0 X X^2+X X^2 X^2+X X X X^2+X 0 X X^2+X 0 X X^2 X X X^2 X 0 X X^2+X X^2+X X 0 0 0 X 0 X X X 0 X^2+X X^2 X X^2+X 0 X 0 X X X^2+X X^2 0 X^2+X X^2 0 X^2 X^2 X^2 X X^2 X X^2 X^2+X X 0 X^2+X X^2+X X^2 X^2 X^2 X^2+X X X X^2+X X^2+X X X^2 X X^2+X X^2+X X^2 X 0 X^2 X^2 X^2+X X^2+X X^2 X^2 X^2 0 X^2+X 0 X^2 X^2 X X^2+X X X^2 0 X X 0 0 0 0 X X 0 X X^2+X X 0 X X^2 X^2+X X^2+X X 0 X X^2 X^2 0 X^2 0 X X 0 X X^2 X^2 0 X^2+X X^2 X^2+X X X^2 X^2+X X X^2 0 0 X^2 0 X X^2+X X^2 0 X^2+X X^2+X X^2 X^2 X^2+X 0 X^2 X^2+X X^2+X X^2 X X^2+X X^2 X^2 0 X^2+X X X^2+X 0 X 0 0 0 0 X^2+X 0 0 0 0 0 X^2 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 0 0 0 X^2 X^2 0 X^2 0 0 X^2 X^2 0 X^2 0 0 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 0 0 X^2 X^2 0 X^2 0 0 0 X^2 0 X^2 0 0 0 0 0 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 X^2 0 X^2 0 0 0 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 0 X^2 0 0 X^2 X^2 X^2 0 0 0 X^2 0 0 X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 0 X^2 0 generates a code of length 71 over Z2[X]/(X^3) who´s minimum homogenous weight is 61. Homogenous weight enumerator: w(x)=1x^0+68x^61+138x^62+204x^63+282x^64+346x^65+394x^66+460x^67+549x^68+662x^69+705x^70+708x^71+784x^72+612x^73+538x^74+492x^75+286x^76+260x^77+196x^78+140x^79+107x^80+74x^81+60x^82+32x^83+37x^84+26x^85+16x^86+12x^87+2x^88+1x^102 The gray image is a linear code over GF(2) with n=284, k=13 and d=122. This code was found by Heurico 1.16 in 59.9 seconds.