The generator matrix

 1  0  1  1  1 X^3+X^2+X  1  X  1 X^3  1  1 X^2  1  1  1 X^2+X  1  1 X^3+X^2  1 X^3+X  1  1  1  1  1  1  0 X^2+X  1  1  1  1  1 X^3 X^3+X^2+X  1  1  1 X^3  1  1  1 X^2 X^3+X^2+X  1 X^3+X  X  X X^3+X^2  1  1  1  1  1  1  X  0  1  1  1  1  X  0
 0  1 X+1 X^2+X X^3+X^2+1  1 X^3+X^2  1 X^2+X+1  1 X^3+X  1  1 X^3 X+1 X^3+X^2+X  1 X^3+X^2+X+1 X^2  1  X  1 X+1 X^3+X^2+X+1 X^2+1 X^3+1 X^2+1  0  1  1 X^3+X^2+X X^3+X+1 X^3+X^2+1 X^2 X^2+X  1  1 X^3+X^2+1 X^3+1 X^2  1 X^3+X X^2 X^2+X  1  1 X^3+X+1  1  0  0  X X^3+X^2+X X^3  X X^3+1 X^3+1 X^3+X^2  1  1 X^3+X^2+X+1 X^3+X^2+X+1 X^3+X^2+X+1 X^2+X+1 X^3+X  1
 0  0 X^2  0 X^3+X^2 X^2  0 X^2 X^3+X^2 X^3+X^2  0 X^2 X^3+X^2 X^2 X^3 X^3+X^2  0 X^3 X^2  0 X^3+X^2  0 X^3 X^3  0 X^3 X^3  0  0  0 X^3+X^2 X^2 X^3+X^2 X^2 X^3 X^2 X^2  0 X^3+X^2 X^3+X^2 X^3 X^3  0 X^2 X^2 X^3 X^2 X^2 X^2 X^3 X^3+X^2 X^3 X^2 X^2 X^3  0 X^3 X^3 X^3 X^3  0 X^2 X^3+X^2 X^3  0
 0  0  0 X^3  0  0  0  0 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3 X^3  0  0 X^3  0  0 X^3  0  0 X^3  0 X^3  0 X^3  0 X^3  0  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0  0  0 X^3  0 X^3 X^3 X^3  0  0  0
 0  0  0  0 X^3  0 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0 X^3 X^3  0  0 X^3  0  0 X^3 X^3  0 X^3  0 X^3 X^3  0  0 X^3  0 X^3 X^3  0 X^3 X^3  0  0  0  0  0 X^3 X^3 X^3 X^3  0  0 X^3  0 X^3 X^3  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0 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+121x^60+334x^61+262x^62+654x^63+408x^64+702x^65+380x^66+500x^67+248x^68+320x^69+85x^70+30x^71+15x^72+14x^73+5x^74+2x^76+6x^77+1x^78+4x^80+3x^82+1x^84

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 0.453 seconds.