The generator matrix

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

generates a code of length 64 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 59.

Homogenous weight enumerator: w(x)=1x^0+86x^59+646x^60+672x^61+1481x^62+984x^63+1336x^64+682x^65+902x^66+322x^67+442x^68+256x^69+246x^70+64x^71+54x^72+6x^73+10x^74+1x^78+1x^80

The gray image is a code over GF(2) with n=512, k=13 and d=236.
This code was found by Heurico 1.16 in 0.75 seconds.