The generator matrix

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

generates a code of length 72 over Z4[X]/(X^2+2X+2) 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 0.468 seconds.