The generator matrix

 1  0  1  1  1 X^3+X^2+X  1  1  0  1 X^3+X^2+X  1  1  1  1 X^3  1 X^3+X  1  1  0  1 X^3+X  1  1  1  1  1 X^3+X^2  X  1  1  1  1 X^2  1  1 X^3+X  1  1 X^2  1  1  1  1  X  1 X^3+X X^3  X X^2  X  0  1 X^3+X^2  X  1 X^3+X^2+X X^2+X  1  1  1  X  1  1
 0  1 X+1 X^3+X^2+X X^2+1  1 X^3+X^2+1  0  1 X^3+X^2+X  1 X+1 X^3+1 X^2+X+1 X^3  1 X^3+X  1 X^3+X^2+X+1  0  1 X^3+X  1  1 X^3+X^2+X+1 X^3+X^2+1 X+1 X^2  1  1  X X^3+X^2+X+1 X^3+X^2+1 X^2  1  1 X^3+X  1 X^3+1 X+1  1 X^3+X^2 X^3+X^2+X+1 X^3+1 X^2+X+1 X^2 X^3+1  1  1 X^3+X  1 X^3+X^2+X  1 X^3+X^2+X+1  1  0  X  1  1 X^3+1 X^3 X^3+X+1 X^2+X X^3+X^2+X+1 X^3
 0  0 X^2  0  0  0  0 X^2 X^3+X^2 X^3+X^2 X^2 X^3+X^2 X^3 X^2 X^3+X^2 X^2 X^3 X^3 X^2 X^3 X^3 X^2 X^3+X^2 X^3 X^3+X^2 X^2  0  0 X^2 X^3+X^2 X^3+X^2  0 X^2 X^3  0 X^2 X^3  0 X^3+X^2 X^3 X^3+X^2 X^2 X^3+X^2 X^3+X^2 X^3 X^3  0 X^2  0 X^2 X^3 X^3 X^3+X^2  0 X^2 X^2 X^3 X^3 X^2  0 X^3 X^3 X^2  0 X^2
 0  0  0 X^3+X^2 X^3 X^3+X^2 X^2 X^2 X^3+X^2 X^3  0 X^3+X^2  0 X^3  0 X^3 X^3 X^3 X^3+X^2 X^3+X^2 X^3+X^2 X^2 X^3+X^2 X^2 X^2  0 X^3 X^3+X^2 X^2  0  0 X^2 X^3+X^2 X^3  0 X^3 X^3+X^2 X^2 X^3+X^2  0 X^3 X^2 X^3 X^2 X^2 X^3+X^2 X^2 X^2 X^3+X^2 X^3+X^2 X^2 X^2  0 X^3+X^2 X^3+X^2 X^3 X^2 X^3+X^2 X^3+X^2  0  0 X^3+X^2 X^3 X^3  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+61x^60+312x^61+454x^62+528x^63+531x^64+488x^65+514x^66+404x^67+423x^68+232x^69+34x^70+56x^71+18x^72+24x^73+2x^74+4x^75+2x^76+1x^80+4x^82+2x^84+1x^88

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 0.391 seconds.