The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+494x^59+1100x^60+1822x^61+1866x^62+2256x^63+2044x^64+2084x^65+1611x^66+1296x^67+795x^68+586x^69+189x^70+118x^71+55x^72+36x^73+11x^74+10x^75+5x^76+1x^78+2x^79+2x^82

The gray image is a code over GF(2) with n=512, k=14 and d=236.
This code was found by Heurico 1.16 in 3.02 seconds.