The generator matrix

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

generates a code of length 73 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 67.

Homogenous weight enumerator: w(x)=1x^0+86x^67+653x^68+1182x^69+1834x^70+1720x^71+2072x^72+1864x^73+2152x^74+1548x^75+1301x^76+764x^77+553x^78+310x^79+193x^80+60x^81+47x^82+14x^83+12x^84+2x^85+13x^86+2x^87+1x^90

The gray image is a code over GF(2) with n=584, k=14 and d=268.
This code was found by Heurico 1.16 in 3.25 seconds.