The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+558x^58+944x^59+2090x^60+1632x^61+2232x^62+1872x^63+2322x^64+1576x^65+1476x^66+728x^67+589x^68+152x^69+130x^70+8x^71+45x^72+18x^74+9x^76+2x^78

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 15.8 seconds.