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

generates a code of length 63 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+64x^57+133x^58+290x^59+340x^60+430x^61+571x^62+566x^63+592x^64+430x^65+251x^66+142x^67+113x^68+70x^69+34x^70+28x^71+4x^72+10x^73+2x^74+12x^75+5x^76+4x^77+1x^78+2x^79+1x^96

The gray image is a code over GF(2) with n=504, k=12 and d=228.
This code was found by Heurico 1.16 in 0.609 seconds.