The generator matrix

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

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+22x^66+98x^67+442x^68+316x^69+469x^70+318x^71+813x^72+280x^73+540x^74+270x^75+333x^76+108x^77+54x^78+18x^79+8x^80+1x^82+1x^88+1x^90+1x^92+1x^94+1x^96

The gray image is a code over GF(2) with n=576, k=12 and d=264.
This code was found by Heurico 1.16 in 0.469 seconds.