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 X 1 X 1 X X 1 1 1 1 1 X 1 1 X 1 X^2 1 1 0 X 1 X 1 1 1 X^2 X X X^2 X X 1 X^2 X^2 1 X 0 1 0 X 0 0 0 X X^2+X X 0 X^2 X^2 0 X X^2+X X X^2+X X^2+X X^2+X X^2+X X^2 0 0 X^2+X X^2 X^2+X 0 X^2 X X X^2 X X 0 X^2+X X^2 0 X X^2+X 0 X^2+X X^2 X^2+X 0 X X^2+X X^2 X^2+X X^2 X 0 X^2 X^2 0 0 X^2+X X^2+X X^2+X 0 X X^2+X X^2+X 0 X^2+X X 0 X X X^2+X X X^2 X^2 0 0 X 0 X X X^2+X 0 0 0 X^2+X X^2+X X X X^2 0 X X^2 0 X^2+X X^2+X X^2 X^2+X X^2 0 X^2 X X^2 X X X X^2 0 0 X X^2 X X^2 X^2+X X^2+X X^2+X X 0 X^2 X X^2 X 0 X^2+X 0 0 0 X X^2+X X^2 0 X X X^2+X 0 X^2+X 0 X^2+X X^2 X^2 X X^2 X^2 X X^2 0 0 0 0 X X 0 X^2+X X X^2 X^2+X X X^2 X^2 X X X^2 0 X^2+X 0 X X^2 X X 0 0 X X^2 X^2+X X^2+X X X X^2+X X^2+X X^2+X 0 X^2 0 0 X^2 X^2 X 0 X^2+X X X^2 X X^2+X X^2+X X 0 X X X^2 X X^2 X^2 X^2 X^2+X 0 X^2+X X X X^2 0 X^2+X X^2 X X^2+X X^2 X X 0 0 0 0 X^2 0 0 0 X^2 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 0 0 X^2 X^2 0 0 0 X^2 X^2 0 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 0 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 0 0 X^2 0 X^2 0 0 X^2 X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 0 X^2 0 0 0 X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 0 0 0 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 0 0 X^2 0 0 0 0 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 0 X^2 0 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 0 0 0 0 generates a code of length 71 over Z2[X]/(X^3) who´s minimum homogenous weight is 62. Homogenous weight enumerator: w(x)=1x^0+49x^62+100x^63+181x^64+132x^65+296x^66+134x^67+485x^68+98x^69+561x^70+150x^71+565x^72+110x^73+459x^74+90x^75+231x^76+70x^77+124x^78+82x^79+53x^80+30x^81+41x^82+16x^83+16x^84+8x^85+5x^86+4x^87+4x^88+1x^102 The gray image is a linear code over GF(2) with n=284, k=12 and d=124. This code was found by Heurico 1.16 in 1.59 seconds.