The generator matrix

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

generates a code of length 68 over Z2[X]/(X^4) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+39x^66+232x^67+67x^68+72x^69+45x^70+32x^71+16x^72+4x^74+4x^76

The gray image is a linear code over GF(2) with n=544, k=9 and d=264.
This code was found by Heurico 1.16 in 0.172 seconds.