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  X  1  X  X  X  1  1  X  X  1  X  1  X  X  X  X  X  X  X  1  1  1  1 X^2  0 X^2  0 X^2  0 X^2 X^3  X  X X^2  1  1 X^2  0 X^3  1 X^2 X^3 X^2  1
 0 X^3+X^2  0 X^3+X^2  0 X^3+X^2  0 X^3+X^2 X^3 X^2 X^3 X^2 X^3 X^2 X^3 X^2  0 X^3+X^2  0 X^3+X^2  0 X^3+X^2  0 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^3 X^3  0  0 X^3  0 X^3 X^2 X^2 X^2 X^2 X^3 X^3 X^3 X^2 X^2 X^2 X^2 X^3+X^2 X^2 X^3+X^2 X^2 X^3+X^2 X^2 X^2 X^2  0 X^3 X^3+X^2  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^3
 0  0 X^3  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0  0  0  0  0  0 X^3 X^3 X^3  0 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0 X^3 X^3  0  0 X^3 X^3  0 X^3 X^3  0  0  0  0 X^3 X^3  0  0 X^3 X^3  0  0 X^3  0  0  0 X^3  0 X^3 X^3 X^3  0 X^3
 0  0  0 X^3 X^3 X^3 X^3  0  0  0 X^3 X^3 X^3 X^3  0  0  0  0 X^3 X^3 X^3 X^3  0  0  0 X^3 X^3  0  0 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3  0  0 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3  0 X^3  0  0 X^3  0  0  0  0 X^3 X^3 X^3  0 X^3 X^3  0  0  0

generates a code of length 67 over Z2[X]/(X^4) who´s minimum homogenous weight is 65.

Homogenous weight enumerator: w(x)=1x^0+8x^65+60x^66+112x^67+62x^68+8x^69+1x^72+1x^78+2x^82+1x^86

The gray image is a linear code over GF(2) with n=536, k=8 and d=260.
This code was found by Heurico 1.16 in 0.266 seconds.