The generator matrix

 1  0  0  1  1  1 X^3  1  1  0 X^2  1  1 X^3+X  X  1  1  1  1 X^3 X^3+X  1 X^2+X  1 X^2  1  1 X^3+X^2+X  1  1  X X^3+X^2  1  X X^3+X^2  1  1  1 X^3+X^2  1  1  1  1  1  1 X^3  1  1  1  1  0  X  1  1 X^2+X  1 X^3+X  1 X^2  1 X^3+X^2+X X^3+X^2+X X^2  1
 0  1  0 X^3 X^2+1 X^3+X^2+1  1  X X^3+X  X  1 X^3+X+1 X+1  1  1 X^3+X^2+1  0 X^2+X+1 X^2  1  X  1  1  0  1 X^2+X+1 X^3+X^2  1 X^3+X^2+X+1 X^2+X X^2  1 X^2+X  1  0 X^3+X^2+X+1 X^3  1 X^3+X  X X^2+X+1 X^2+X X^3+X^2 X^2+X+1 X^3+X^2+X+1  1 X^2+X X^3+X X^2+1 X^3+X+1  1  1  1 X+1 X^3 X^2  1  X  1 X^2+X  1  1  1 X^3
 0  0  1 X^3+X+1 X+1 X^3 X^3+X+1 X^3+X X^3+1  1  X  1 X^3+X^2+X X+1  X X^3+X^2+X  X X^3+X^2+X+1 X^3+X^2+1 X^3+X^2+1  1  1 X^2 X^2+X X^2+1 X^2 X^3+X^2 X^3+X^2+1 X^2+1 X^3+X^2+X+1  1 X+1  X X^2+X  1 X^3+X X^3+1 X^2+X+1  1 X^3 X^2+X X^3+X+1 X^3+X+1  0 X+1 X^3+X^2+X X^3+X^2+1 X^2+X X^3+X X^3+X^2+1 X^2 X^2 X^3+X^2  0  1  1  0 X^2 X^3+X^2 X^3 X^3+X^2+X  0 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+103x^60+560x^61+716x^62+688x^63+602x^64+446x^65+256x^66+224x^67+157x^68+166x^69+100x^70+60x^71+8x^72+5x^74+1x^76+3x^78

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 8.28 seconds.