The generator matrix

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

generates a code of length 64 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+128x^57+1012x^58+2524x^59+3821x^60+5510x^61+6758x^62+8960x^63+8343x^64+8892x^65+7021x^66+5706x^67+3428x^68+1782x^69+901x^70+464x^71+148x^72+48x^73+35x^74+24x^75+19x^76+8x^77+1x^78+2x^83

The gray image is a code over GF(2) with n=512, k=16 and d=228.
This code was found by Heurico 1.16 in 35.6 seconds.