The generator matrix

 1  0  0  1  1  1 2X  1  1  1  1  2 2X+2 2X+2  1  1  X 3X+2  1  1 3X+2  1  1  2  1  1 3X  1 3X 3X  1 X+2  1  0  1 3X  1 2X  1  1 X+2  0 2X+2  1  1 3X  1 2X  X  1  0 2X+2  1  X  1 3X+2 2X 3X+2  1  1 X+2  1  1
 0  1  0 2X  3 2X+3  1  X X+3 3X 3X+3  1  X  1  0  3  1 2X+2 X+2  1  1 3X+1  X  1 2X X+3  1 X+2  1 X+2  1  1 3X+3  2 2X+2  X X+2  1 3X+1 2X+1  1  1 3X+2 3X 2X+3  2 3X+1 3X+2  1  0  1 2X+2 2X+2  0 3X+1 3X  1  1 2X+3 3X+1  0 2X  0
 0  0  1 3X+1 X+1 2X X+1  X 2X+1  1 3X 3X  1 X+1  X 2X+1 X+2  1 3X+3 3X+2 3X+3  2 2X+2  1  1 3X+3 3X  3  2  1 2X+3  1 2X  1  1  1 2X 2X+3 X+2 X+1 2X+3  2  1 3X+1 2X+2  1 X+1  1 X+3 X+3 X+3  1  2  1 2X+3  1 3X+2  2 3X+2 X+3  1  2  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+156x^59+466x^60+788x^61+666x^62+570x^63+414x^64+332x^65+240x^66+166x^67+97x^68+92x^69+60x^70+40x^71+4x^72+1x^74+2x^76+1x^78

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 0.219 seconds.