The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+159x^64+1184x^65+2869x^66+4668x^67+7453x^68+10656x^69+14235x^70+15800x^71+17382x^72+15958x^73+14121x^74+10498x^75+7445x^76+4532x^77+2318x^78+914x^79+468x^80+248x^81+80x^82+36x^83+20x^84+12x^85+9x^86+2x^87+2x^89+2x^91

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 162 seconds.