The generator matrix

 1  0  0  1  1  1  0 X^3  1  1 X^3 X^2  1  1  1  1 X^3+X X^3+X  1 X^3+X  1  X X^3+X^2+X  1  1 X^3+X  1  1  1  1 X^2  1 X^2+X  1 X^3+X^2 X^3+X X^3+X^2+X X^3+X^2 X^2  X  1  1 X^2+X X^3+X^2  1  1  1 X^3  1 X^3+X  1  1  1 X^3+X^2+X X^3  1  1  1  1 X^2  1  1 X^3+X  1
 0  1  0  0 X^2+1 X^2+1  1 X^3+X^2+X X^3 X^3+X^2+1  1  1 X^3+X^2  1 X^2+X X+1  1 X^2+X  X  1 X+1  1  1 X^3+X X^2+X+1 X^2 X^3+X+1 X^3+X+1 X^3+X^2 X^2+X  1 X^2  1 X^3+X^2  1  1  1  1  1  1 X^3+X^2+X  X  1  0 X^2+1 X^3+X^2+X+1 X^3+X^2+1  1  1  1 X^3+X^2+X+1 X^2+1 X^3+X^2+X  X  1 X^3+X^2+X X^3+X^2 X^2  X  1 X^3  0  1 X+1
 0  0  1 X+1 X^3+X+1 X^3 X^3+X^2+X+1  1 X^3+X^2+X X^2+1  1 X^3+X X^3+X^2+1  X X^3+X+1 X^2 X^3+X^2+1  1  X X^3+X^2+X  1 X+1 X^3 X^3+X^2 X^2+1  1 X^2+X+1 X^3+X  1 X^3+X^2+1 X^3 X^2+X X+1 X+1  1 X^3+X^2 X^2+1 X^3+X^2+X+1  X X^3+X^2+X+1  0 X^3+X^2+1 X^3+X^2+X  1 X^3+X^2+X X^3+X^2 X^3+X^2+X+1 X^3+X^2+X X^3+X+1 X^3  0  1 X^2+X+1  1 X^3+X^2+X+1 X^3+X^2+1  X X^3+X^2 X^2+X X^3+X^2+X X^2 X^3+X^2+X+1 X^2+X X^3+X^2+X
 0  0  0 X^3 X^3  0 X^3 X^3 X^3  0  0 X^3  0 X^3  0 X^3 X^3  0  0  0  0  0 X^3 X^3 X^3 X^3  0 X^3 X^3  0 X^3  0  0  0 X^3  0  0  0  0 X^3  0 X^3  0 X^3  0  0 X^3 X^3  0  0 X^3 X^3  0 X^3  0 X^3 X^3 X^3 X^3  0  0 X^3 X^3 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+637x^60+792x^61+1308x^62+1272x^63+1193x^64+824x^65+724x^66+424x^67+441x^68+176x^69+228x^70+96x^71+62x^72+12x^74+1x^76+1x^84

The gray image is a linear code over GF(2) with n=512, k=13 and d=240.
This code was found by Heurico 1.16 in 141 seconds.