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

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+303x^60+48x^61+551x^62+392x^63+647x^64+416x^65+563x^66+368x^67+409x^68+48x^69+221x^70+8x^71+72x^72+41x^74+7x^76+1x^100

The gray image is a linear code over GF(2) with n=520, k=12 and d=240.
This code was found by Heurico 1.16 in 0.797 seconds.