The generator matrix

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

generates a code of length 73 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+208x^64+1112x^65+2726x^66+5678x^67+9081x^68+14812x^69+21179x^70+26894x^71+31591x^72+34416x^73+32595x^74+28254x^75+20793x^76+14696x^77+8959x^78+4858x^79+2364x^80+1168x^81+451x^82+164x^83+80x^84+32x^85+8x^86+8x^87+8x^88+2x^92+4x^93+2x^94

The gray image is a code over GF(2) with n=584, k=18 and d=256.
This code was found by Heurico 1.16 in 612 seconds.