The generator matrix

 1  0  0  0  1  1  1  1 X^2  1 X^2+X  1  1  0  X  1  0  1  1  1  1 X^2  X  0  X  1  X  1  1  1  0  X  1  1  X X^2+X  1 X^2 X^2  X  1  1  1  1  1  X X^2  0 X^2+X  1  0  1  1  X  0  1  X X^2 X^2  1 X^2+X  1 X^2+X  1  X  1  0  1  1  1  X
 0  1  0  0  X  X X^2+X X+1  0 X+1  1 X^2+1 X^2+1  1  1  0 X^2+X  1 X^2 X^2+X+1 X^2+X  1  1  1  X  0  1 X+1 X+1 X^2+1  1  X  1 X^2+X+1 X^2  X  X  1 X^2+X  1  X X^2  1 X^2  1  1  1  X  1 X^2+X+1  1 X^2+X+1 X^2+1  1  1  X  0  0 X^2  1  0  0  0 X^2+1  1 X^2+X+1  0 X^2+1 X+1 X+1  1
 0  0  1  0  X X^2+X+1 X^2+X+1 X+1  1 X^2+X+1 X^2+1 X^2+X  0 X+1 X^2 X^2+X X^2+X X+1  X  0 X^2+1  X X+1  1  1 X^2+1 X^2+X X^2 X^2+X  1 X+1  1  1 X+1  0  1  0  X  0  1 X^2 X^2+X+1 X+1  1  0 X^2+1  1  1 X^2  X  0  1  1 X^2+X+1  X X+1  X X^2  1  0  1  X  0 X+1 X+1 X+1 X^2+X X+1  X  1 X+1
 0  0  0  1 X+1 X^2+X+1  X X^2+X+1  1 X^2+X X^2+1  0 X+1 X^2+X X+1  X  1  1 X^2+X+1  X X^2+X X^2+X X^2 X^2+X+1 X^2 X^2+X+1  1 X+1 X^2 X^2+X  0  1 X^2+1 X^2  1  0  X X+1  1 X+1 X^2+1 X+1 X+1 X^2+X+1 X+1 X^2  X X+1 X+1  0  X X^2+1  0 X^2+X+1  0  0  1  1 X^2+1 X^2+X  1  0  1  0 X^2+1 X^2  1  X X^2+X+1 X^2+X X+1
 0  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2  0  0 X^2  0 X^2 X^2  0 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2  0  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+226x^64+392x^65+628x^66+614x^67+788x^68+620x^69+780x^70+590x^71+777x^72+490x^73+575x^74+402x^75+405x^76+264x^77+281x^78+148x^79+100x^80+50x^81+37x^82+4x^83+7x^84+8x^85+3x^86+2x^87

The gray image is a linear code over GF(2) with n=284, k=13 and d=128.
This code was found by Heurico 1.16 in 7.27 seconds.