The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+182x^63+1052x^64+2736x^65+5342x^66+9320x^67+14429x^68+21150x^69+26382x^70+33766x^71+33194x^72+33412x^73+27392x^74+21932x^75+14007x^76+8830x^77+4993x^78+2210x^79+963x^80+486x^81+204x^82+92x^83+34x^84+22x^85+7x^86+2x^87+2x^89+2x^93

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 669 seconds.