The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  1  1  1  1  1  1  1  1  X  1  1 2X+2  1  1 2X  2  0  1  1  1 2X  X  X  2  X  0 2X  2  X  0  X
 0  X  0  X 2X  0 X+2 3X+2  0  X 3X 2X X+2 X+2  0  0  2  X 3X+2  2  2 2X+2 3X X+2 2X+2  X 3X  0 2X+2  X X+2  2  2 X+2  X 2X+2 2X  0 2X 3X 3X 3X+2 3X 3X+2  X 2X+2 2X+2  X  X  X 2X  X  2  2 3X+2  X  X 3X+2  0  0 2X+2 X+2  X 3X
 0  0  X  X  0 3X+2 X+2 2X X+2  X 2X  2 X+2  0 3X  2  2 X+2 2X+2  X 2X+2 X+2 3X+2  2  0  2 3X+2  X 2X+2  2  X 3X  X 3X  2  0 X+2 2X+2 3X  X  X X+2  2 2X 2X+2 3X 2X+2 2X+2 X+2  X  0  0  X  X 2X  2  0 3X+2  X 2X  X  2 3X+2  0
 0  0  0  2  2  2 2X  2  0 2X 2X+2  0 2X+2  0 2X+2  2  0  2  2 2X  2 2X+2  0  0 2X  2 2X  2 2X+2 2X  2  0 2X+2 2X 2X+2 2X+2 2X+2 2X 2X 2X+2  0 2X+2  0 2X  2  2 2X  0 2X 2X+2 2X  2  0 2X 2X+2  0 2X+2  2  2  2  0  0  0  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+208x^59+266x^60+512x^61+394x^62+508x^63+464x^64+632x^65+274x^66+326x^67+160x^68+146x^69+67x^70+88x^71+37x^72+4x^73+6x^75+2x^77+1x^94

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 4.86 seconds.