The generator matrix

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

generates a code of length 72 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+171x^64+1232x^65+2499x^66+5312x^67+7263x^68+11262x^69+12656x^70+16772x^71+16217x^72+17560x^73+13105x^74+11428x^75+6936x^76+4638x^77+2118x^78+1166x^79+341x^80+190x^81+112x^82+56x^83+11x^84+12x^85+4x^86+2x^87+4x^88+2x^89+2x^90

The gray image is a code over GF(2) with n=576, k=17 and d=256.
This code was found by Heurico 1.16 in 161 seconds.