The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+132x^59+578x^60+662x^61+710x^62+512x^63+488x^64+346x^65+218x^66+124x^67+123x^68+80x^69+79x^70+28x^71+10x^72+1x^74+4x^77

The gray image is a code over GF(2) with n=504, k=12 and d=236.
This code was found by Heurico 1.16 in 0.235 seconds.