The generator matrix

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

generates a code of length 72 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 63.

Homogenous weight enumerator: w(x)=1x^0+124x^63+1083x^64+2664x^65+5537x^66+9360x^67+14581x^68+19912x^69+28949x^70+30840x^71+34940x^72+32248x^73+29021x^74+20528x^75+14799x^76+8524x^77+4882x^78+2282x^79+1134x^80+404x^81+176x^82+74x^83+50x^84+4x^85+11x^86+4x^87+4x^88+4x^89+2x^91+2x^95

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 639 seconds.