The generator matrix

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

generates a code of length 72 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 63.

Homogenous weight enumerator: w(x)=1x^0+144x^63+930x^64+2378x^65+5451x^66+9132x^67+14297x^68+20468x^69+28056x^70+32254x^71+34892x^72+33378x^73+28714x^74+20736x^75+14319x^76+8380x^77+4693x^78+2222x^79+1025x^80+378x^81+173x^82+32x^83+38x^84+24x^85+17x^86+8x^87+2x^88+2x^89

The gray image is a code over GF(2) with n=576, k=18 and d=252.
This code was found by Heurico 1.16 in 623 seconds.