The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+710x^66+968x^67+2695x^68+2296x^69+4222x^70+3504x^71+4797x^72+3416x^73+3902x^74+2112x^75+1960x^76+832x^77+858x^78+168x^79+209x^80+16x^81+68x^82+33x^84+1x^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 241 seconds.