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

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+72x^58+168x^59+180x^60+404x^61+368x^62+684x^63+418x^64+768x^65+260x^66+408x^67+125x^68+76x^69+52x^70+52x^71+34x^72+12x^74+4x^76+4x^78+3x^80+2x^84+1x^100

The gray image is a code over GF(2) with n=512, k=12 and d=232.
This code was found by Heurico 1.16 in 0.641 seconds.