The generator matrix

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

generates a code of length 64 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+393x^58+1014x^59+2274x^60+2728x^61+3886x^62+4266x^63+4379x^64+4096x^65+3662x^66+2408x^67+1923x^68+828x^69+467x^70+226x^71+122x^72+40x^73+31x^74+6x^75+5x^76+4x^77+9x^78

The gray image is a code over GF(2) with n=512, k=15 and d=232.
This code was found by Heurico 1.16 in 10.5 seconds.