The generator matrix

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

generates a code of length 72 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 65.

Homogenous weight enumerator: w(x)=1x^0+210x^65+1446x^66+2618x^67+4381x^68+5218x^69+7533x^70+7188x^71+8776x^72+7194x^73+7599x^74+5186x^75+4077x^76+1924x^77+1251x^78+530x^79+198x^80+120x^81+43x^82+12x^83+6x^84+6x^85+16x^86+2x^87+1x^88

The gray image is a code over GF(2) with n=576, k=16 and d=260.
This code was found by Heurico 1.16 in 39 seconds.