The generator matrix

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

generates a code of length 64 over Z2[X]/(X^4) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+364x^60+336x^61+739x^62+374x^63+630x^64+304x^65+671x^66+296x^67+296x^68+24x^69+12x^70+10x^71+16x^72+16x^74+4x^76+1x^82+1x^86+1x^88

The gray image is a linear code over GF(2) with n=512, k=12 and d=240.
This code was found by Heurico 1.16 in 0.438 seconds.