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

generates a code of length 67 over Z2[X]/(X^4) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+51x^66+144x^67+51x^68+1x^70+4x^74+4x^76

The gray image is a linear code over GF(2) with n=536, k=8 and d=264.
This code was found by Heurico 1.16 in 0.266 seconds.