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

generates a code of length 65 over Z2[X]/(X^4) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+169x^60+48x^61+224x^63+381x^64+480x^65+256x^66+224x^67+137x^68+48x^69+74x^72+5x^76+1x^116

The gray image is a linear code over GF(2) with n=520, k=11 and d=240.
This code was found by Heurico 1.16 in 2.36 seconds.