The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+157x^64+1212x^65+2674x^66+4818x^67+7641x^68+11282x^69+12775x^70+16678x^71+16263x^72+17312x^73+13646x^74+10750x^75+7050x^76+4696x^77+2238x^78+1108x^79+417x^80+196x^81+85x^82+32x^83+23x^84+6x^85+3x^86+2x^87+1x^90+4x^91+2x^94

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 150 seconds.