The generator matrix

 1  0  0  0  1  1  1 X^2  0  1  1  X  1  0  1  0  X  1 X^2+X  0  X  1  1  1 X^2+X  1 X^2  1  X  X  1  1  1  1 X^2+X  X  1 X^2  1  1 X^2  1  1  1  0  X  1 X^2+X  1 X^2  1 X^2  1 X^2+X  0  1  1  1  X X^2+X  1  1 X^2+X  0  1  1 X^2 X^2+X  1  1  1
 0  1  0  0  1 X^2  1  0  1  0 X+1  1 X+1  1  X X^2  1  X  1  1  X  X  0 X^2+1  0 X^2+X  1  X  1  X X+1 X^2+X X^2+1 X^2+X+1  1 X^2+X X^2 X^2+X X^2+1  X X^2+X X^2+X+1 X^2+1  0  1 X^2 X^2+1 X^2 X+1  0 X^2+X X^2+X  X  X  1 X^2+1 X^2+X X+1  1  1 X^2+X+1 X^2 X^2+X  1 X+1 X^2+1 X^2 X^2 X^2+X X^2+X+1 X^2
 0  0  1  0  X  0 X^2+X  1  X X^2+1 X^2+X+1 X^2+1  1 X^2+1 X+1 X^2+X X^2  0 X^2+X  1  1 X^2  1  X  1 X^2+X+1  0 X^2+1  1  0 X^2+1 X^2 X^2+1  X  0  1 X^2+X  1 X^2 X^2+1  1  X  1  0 X^2+X+1  1 X+1  1 X^2  1 X^2+1  X  1  1  0  X X^2+X X^2+1 X^2+1 X^2  0 X^2+X  1 X+1  X  1 X^2+X  1 X^2+X  0  0
 0  0  0  1  X  1 X+1  1 X+1 X^2 X^2+X X^2 X^2+1  1 X+1  1  X X^2+1 X^2+1 X^2+X+1  0  X  X  1 X^2+X+1 X^2+X  X X^2+X+1 X^2+X  1 X^2+X X^2+X+1  1  1  1 X+1 X^2  X X^2+X  0 X^2+X+1 X^2+X+1 X+1 X^2+X+1 X^2+X+1 X^2+1 X^2+X+1  0  X X^2+X X+1  1  1 X^2+X X^2+1 X^2+X X^2  0 X^2+1  1 X^2+X X^2+X+1 X^2+1  1 X^2 X^2  1 X+1  X X^2+1 X^2
 0  0  0  0 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2  0  0  0 X^2  0  0 X^2  0  0 X^2  0 X^2  0  0  0 X^2 X^2 X^2  0 X^2  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2  0  0 X^2  0  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0

generates a code of length 71 over Z2[X]/(X^3) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+259x^64+348x^65+674x^66+468x^67+865x^68+536x^69+1004x^70+552x^71+715x^72+456x^73+678x^74+308x^75+495x^76+248x^77+220x^78+96x^79+137x^80+44x^81+44x^82+16x^83+24x^84+4x^86

The gray image is a linear code over GF(2) with n=284, k=13 and d=128.
This code was found by Heurico 1.11 in 1.2 seconds.