The generator matrix

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

generates a code of length 72 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+716x^66+1076x^67+2604x^68+2452x^69+4032x^70+3492x^71+4819x^72+3472x^73+3618x^74+2232x^75+2062x^76+860x^77+828x^78+204x^79+155x^80+32x^81+86x^82+4x^83+18x^84+5x^88

The gray image is a code over GF(2) with n=576, k=15 and d=264.
This code was found by Heurico 1.16 in 465 seconds.