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  2  1  1  1  1  1  1  1 2X+2  1  1  X  1  1  1  X  1  1  1  X  1  0 2X+2  1  X  X  1  0  1  X  X  1  X  1 2X  1
 0  X  0  X 2X  0 X+2 3X+2  0 2X 3X 3X  0 3X+2 2X+2  X 2X+2 X+2 X+2 2X+2 3X+2 3X 2X+2  2 3X 2X+2 3X 2X  0 X+2 2X X+2 2X+2 3X  0  X  2 3X X+2  X 3X+2 3X  0  X 3X+2 2X+2  X  X  X  X  0 X+2 2X+2 2X+2  X X+2 3X+2 2X+2 2X X+2 3X+2  X  0
 0  0  X  X  0 3X+2 X+2 2X  2 3X+2 3X+2  2 2X+2  2  X  X 3X+2 3X  0 2X  X  0 3X  2  0 2X X+2  X X+2  2 2X 3X 3X+2 2X+2  X 2X 3X+2  2  2 3X 2X+2 3X 3X X+2 2X  2 3X+2 2X 3X  2 2X+2 3X 3X 3X  0 X+2 2X+2 3X X+2 2X X+2  0 X+2
 0  0  0  2 2X+2  2 2X  2  2  0  2 2X+2  0  0 2X+2 2X  2 2X+2  0  2  0  2  0  0 2X 2X 2X 2X+2 2X+2 2X+2  2  2  0  0  2 2X 2X  2  2  0  2 2X+2 2X  0 2X+2 2X+2 2X+2 2X 2X+2  2 2X 2X  0  2  2 2X+2  0 2X 2X+2  0 2X 2X 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+190x^58+236x^59+411x^60+458x^61+511x^62+690x^63+436x^64+482x^65+246x^66+126x^67+153x^68+34x^69+65x^70+18x^71+23x^72+2x^73+11x^74+2x^75+1x^98

The gray image is a code over GF(2) with n=504, k=12 and d=232.
This code was found by Heurico 1.16 in 0.641 seconds.