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  X  X  1  1  X  X  X  X  1  1  1  1  1  1  1  1  X  X  X  X X^2  0  X  X  X  X X^2  0 X^2 X^2 X^2 X^2 X^3 X^3 X^2  X  X  1  1  1  1 X^2  1  1  1
 0 X^3+X^2  0 X^3+X^2 X^3 X^2 X^3 X^2  0 X^3+X^2  0 X^3+X^2 X^3 X^2 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^2 X^2  0 X^3  0 X^3+X^2 X^3 X^2  0 X^3+X^2 X^3 X^2 X^3+X^2 X^3+X^2  0 X^3 X^3+X^2 X^2  0 X^3 X^2 X^2 X^3+X^2 X^2  0 X^3 X^2 X^2 X^2 X^2 X^3  0 X^3  0  0 X^3 X^3  0 X^3+X^2 X^3+X^2 X^2
 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  0 X^3 X^3 X^3 X^3 X^3  0  0  0 X^3  0 X^3 X^3  0  0  0  0 X^3 X^3 X^3 X^3  0 X^3  0  0  0 X^3 X^3 X^3 X^3  0 X^3  0 X^3 X^3 X^3  0 X^3  0  0  0  0  0 X^3 X^3  0  0  0 X^3 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+6x^66+100x^67+6x^68+1x^70+12x^71+1x^72+1x^78

The gray image is a linear code over GF(2) with n=536, k=7 and d=264.
This code was found by Heurico 1.16 in 0.265 seconds.