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  X  X  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
 0 X^3  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 X^3  0  0 X^3 X^3  0 X^3  0 X^3 X^3 X^3  0 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3  0 X^3 X^3 X^3  0 X^3  0 X^3 X^3 X^3 X^3 X^3  0  0 X^3  0 X^3 X^3  0 X^3 X^3  0  0
 0  0 X^3  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 X^3  0 X^3 X^3  0  0 X^3  0 X^3  0 X^3 X^3 X^3  0 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3  0 X^3 X^3 X^3  0 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3  0  0 X^3 X^3 X^3 X^3  0
 0  0  0 X^3  0  0  0  0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3  0 X^3 X^3 X^3 X^3  0  0  0  0  0  0  0  0  0  0  0  0  0  0 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0  0 X^3 X^3  0 X^3 X^3  0  0
 0  0  0  0 X^3  0  0  0 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3  0  0  0  0  0  0  0  0  0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3  0 X^3  0 X^3  0 X^3 X^3 X^3 X^3  0 X^3  0 X^3 X^3  0 X^3 X^3  0 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3  0 X^3  0
 0  0  0  0  0 X^3  0 X^3 X^3 X^3  0  0  0  0 X^3 X^3 X^3 X^3  0  0  0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0  0  0 X^3  0 X^3 X^3  0 X^3  0 X^3  0 X^3 X^3  0 X^3  0 X^3 X^3 X^3  0 X^3 X^3  0 X^3  0 X^3 X^3 X^3  0 X^3 X^3  0  0  0
 0  0  0  0  0  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3 X^3  0  0 X^3  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0 X^3  0  0 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0  0  0 X^3 X^3  0  0 X^3 X^3 X^3  0  0 X^3  0 X^3 X^3 X^3  0 X^3  0  0  0 X^3  0  0  0  0

generates a code of length 67 over Z2[X]/(X^4) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+23x^64+32x^65+47x^66+832x^67+32x^68+32x^69+16x^70+8x^72+1x^130

The gray image is a linear code over GF(2) with n=536, k=10 and d=256.
This code was found by Heurico 1.16 in 0.219 seconds.