The generator matrix

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

generates a code of length 64 over Z2[X]/(X^4) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+132x^57+1232x^58+2132x^59+3821x^60+5552x^61+7102x^62+8418x^63+9142x^64+8522x^65+7015x^66+5290x^67+3747x^68+1718x^69+969x^70+408x^71+209x^72+58x^73+33x^74+22x^75+8x^76+2x^77+1x^78+2x^79

The gray image is a linear code over GF(2) with n=512, k=16 and d=228.
This code was found by Heurico 1.16 in 33.8 seconds.