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 X^2 X X X X^2 0 0 X X X^2 1 1 1 X 1 X^2 0 1 1 1 X 1 1 1 1 1 X X^2 X 0 X^2 1 1 0 X 0 0 0 0 0 0 X^2 X^2 X X^2+X X 0 0 X^2 X^2+X X^2+X X X X X 0 X X^2+X X 0 X X^2+X X^2 X^2+X X^2 X^2 X^2+X X 0 0 X X^2 X^2 X^2+X X^2 X X X^2 X X^2+X X X^2+X 0 0 X 0 X^2 0 X^2+X X X 0 X 0 X 0 X^2+X X X X X X X^2 X^2 0 0 X 0 0 0 0 0 0 0 0 0 X^2 X^2+X X^2+X X^2+X X X^2+X X^2+X X X^2 X^2 X^2+X X^2+X 0 0 X X X X^2+X X^2+X X^2+X X^2 X^2 X^2+X X X X^2 X^2 X X 0 X X X X^2 X X^2+X X X^2+X X^2+X 0 X X 0 X X^2 0 X^2 X 0 X X^2 X^2+X X^2+X 0 0 0 X^2 X^2 X^2 0 0 0 X 0 0 X^2 X^2+X X X X X X^2 X^2+X X X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X X^2+X X X^2 X X^2+X X^2+X X X^2+X 0 X^2 0 0 0 X^2+X X^2 X X^2+X 0 0 0 X X^2+X X^2+X X X 0 X^2+X X^2+X X^2+X X X X^2+X 0 0 X^2 0 X^2+X 0 0 X X^2+X X^2 X^2+X 0 0 X^2+X X^2+X 0 0 0 0 X 0 X^2+X X^2+X X X^2 X^2+X X^2+X 0 X X 0 X^2 X 0 X^2+X X^2+X X X^2+X X X^2 X^2 X X^2 X^2 0 X^2+X X^2 0 X^2+X X X^2+X X^2 0 X 0 0 X^2 0 X^2+X X 0 0 X^2+X X^2+X X^2 X X X^2 X^2+X X^2 X 0 X^2+X 0 0 X^2 X^2+X X^2+X 0 X^2+X X^2+X X^2 X^2+X X^2 X^2+X 0 0 0 0 0 0 X X X^2 X^2+X X X^2+X X^2 X X 0 X 0 X^2+X X^2+X 0 X X^2 X^2 X^2+X X^2 X X^2+X X^2+X X^2 X X^2 X^2 X^2+X 0 X X^2+X 0 0 X X 0 X^2+X X^2 0 0 X^2 X^2 0 X^2 X 0 X X 0 0 X^2+X X X^2+X X 0 X^2+X X^2 X^2 0 0 X^2 X X X^2 X X^2 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+84x^61+136x^62+180x^63+276x^64+310x^65+403x^66+512x^67+500x^68+666x^69+826x^70+720x^71+646x^72+608x^73+602x^74+458x^75+307x^76+274x^77+174x^78+126x^79+116x^80+80x^81+63x^82+46x^83+41x^84+24x^85+4x^86+6x^87+2x^89+1x^104 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 7.33 seconds.