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

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+16x^66+64x^67+348x^68+64x^69+15x^70+2x^72+1x^96+1x^102

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 0.297 seconds.