The generator matrix

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

generates a code of length 63 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 59.

Homogenous weight enumerator: w(x)=1x^0+180x^59+123x^60+380x^61+132x^62+460x^63+146x^64+312x^65+88x^66+188x^67+17x^68+12x^69+2x^70+4x^71+1x^72+2x^86

The gray image is a code over GF(2) with n=504, k=11 and d=236.
This code was found by Heurico 1.16 in 0.343 seconds.