The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+74x^58+550x^59+1138x^60+1664x^61+1885x^62+1854x^63+2246x^64+2324x^65+1783x^66+1108x^67+716x^68+504x^69+255x^70+142x^71+52x^72+36x^73+31x^74+10x^75+6x^76+4x^78+1x^80

The gray image is a code over GF(2) with n=512, k=14 and d=232.
This code was found by Heurico 1.16 in 2.91 seconds.