The generator matrix

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

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+145x^58+176x^59+553x^60+336x^61+623x^62+480x^63+581x^64+416x^65+478x^66+112x^67+137x^68+16x^69+32x^70+5x^72+1x^78+1x^80+2x^84+1x^90

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 0.343 seconds.