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

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+62x^64+96x^65+712x^66+96x^67+48x^68+8x^70+1x^128

The gray image is a linear code over GF(2) with n=528, k=10 and d=256.
This code was found by Heurico 1.16 in 0.187 seconds.