The generator matrix

 1  0  0  0  1  1  1  1 X^2  1 X^2+X  X  1 X^2  1  1  1  X  1  1  X  0  1  X  0  1  1  0 X^2+X  1 X^2+X  1  1  X  1 X^2+X  1 X^2  1  1 X^2+X X^2 X^2  0  1  1 X^2  X  X  1  1  1 X^2 X^2+X  1  0  0 X^2  1 X^2  1  1 X^2 X^2+X  0 X^2+X  1  X X^2+X X^2  1
 0  1  0  0  0 X^2  1 X^2+1  1 X^2+X+1 X^2  1  0  1 X^2+1 X^2  1  1  X X+1  1  1 X^2 X^2+X X^2+X X^2+X+1  1 X^2+X  1 X^2+X  X X^2+1  0  1  0  1 X^2+X  1  X X^2+X+1 X^2+X X^2+X  1  1 X^2+1  X  1  1  1 X+1 X^2 X+1  0  1 X+1  0  1  1  1  1  1 X^2+X+1  1  0  1 X^2  0 X^2+X  1  1  0
 0  0  1  0  0 X^2+1  1 X^2+X X+1 X^2+1  1 X^2 X^2+X+1 X^2+1  X  X X^2+X+1 X^2+X+1 X^2 X^2 X+1 X^2+X X^2+1  1  1 X^2+X X^2+X+1 X^2+X  0 X+1  1 X^2+X+1 X^2+X X^2+1  0  X  0 X+1 X+1 X^2  1  0 X^2+1  0 X^2+X X^2+X+1 X^2  0  0 X^2 X+1 X^2+X  1 X^2+X X^2+X+1  1 X^2+1 X^2+X X^2+X  X X^2+X+1 X^2+X+1  X  1  1 X^2  1  1 X^2 X+1  0
 0  0  0  1  1  1 X^2 X+1 X+1 X^2+1 X^2+1 X^2+1  X  X  0 X^2+1 X+1 X+1 X^2  X  0 X^2+X+1 X+1  X  1 X^2+X+1 X^2+1  1 X^2+X  0 X^2 X^2 X^2+X X^2+X  1  0 X^2+X X^2+X+1 X^2+1  0 X+1  1 X^2+X+1 X^2+1 X^2+1 X^2+X  1 X^2 X^2+X+1 X^2  0  1  X X^2+1  0  1 X^2+X+1 X^2+X+1 X^2+X+1  0  X  X X^2+X X^2 X^2+1  1 X+1  1 X^2+X X^2+1  0
 0  0  0  0  X  0  0  0  0  X  X  X X^2+X  X  X X^2+X  X X^2 X^2+X  0  0 X^2 X^2+X X^2+X X^2  X  0 X^2+X X^2+X  0 X^2+X X^2+X  0 X^2 X^2 X^2+X  0  X  X X^2 X^2  0 X^2  X  0 X^2  0 X^2  X  X  0 X^2 X^2 X^2 X^2+X X^2  X  0 X^2+X X^2+X  X X^2  0  X X^2+X  0  X  0 X^2 X^2+X  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+60x^62+332x^63+526x^64+816x^65+858x^66+1230x^67+1044x^68+1536x^69+1132x^70+1532x^71+1172x^72+1528x^73+1032x^74+1124x^75+735x^76+680x^77+382x^78+302x^79+156x^80+98x^81+50x^82+18x^83+13x^84+12x^85+6x^86+6x^87+1x^88+2x^89

The gray image is a linear code over GF(2) with n=284, k=14 and d=124.
This code was found by Heurico 1.13 in 4.22 seconds.