The generator matrix

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

generates a code of length 66 over Z2[X]/(X^4) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+4x^64+142x^65+11x^66+44x^67+11x^68+30x^69+5x^70+8x^71

The gray image is a linear code over GF(2) with n=528, k=8 and d=256.
This code was found by Heurico 1.16 in 0.25 seconds.