The generator matrix

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

generates a code of length 65 over Z2[X]/(X^4) who´s minimum homogenous weight is 65.

Homogenous weight enumerator: w(x)=1x^0+34x^65+17x^66+2x^67+4x^68+2x^69+1x^70+2x^71+1x^72

The gray image is a linear code over GF(2) with n=520, k=6 and d=260.
This code was found by Heurico 1.16 in 0.172 seconds.