The generator matrix

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

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+68x^59+288x^60+450x^61+524x^62+494x^63+606x^64+468x^65+490x^66+304x^67+202x^68+100x^69+53x^70+24x^71+4x^73+2x^74+4x^75+6x^76+2x^77+2x^78+2x^79+1x^80+1x^86

The gray image is a code over GF(2) with n=512, k=12 and d=236.
This code was found by Heurico 1.16 in 0.438 seconds.