The generator matrix

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

generates a code of length 63 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+538x^58+864x^59+2107x^60+1616x^61+2710x^62+1608x^63+2254x^64+1408x^65+1510x^66+784x^67+621x^68+112x^69+184x^70+8x^71+37x^72+14x^74+4x^76+2x^78+2x^82

The gray image is a code over GF(2) with n=504, k=14 and d=232.
This code was found by Heurico 1.16 in 49.9 seconds.