The generator matrix

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

generates a code of length 73 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+132x^68+758x^69+845x^70+1120x^71+1034x^72+1212x^73+766x^74+780x^75+425x^76+478x^77+269x^78+172x^79+59x^80+60x^81+46x^82+24x^83+5x^84+4x^85+1x^86+1x^94

The gray image is a code over GF(2) with n=584, k=13 and d=272.
This code was found by Heurico 1.16 in 0.953 seconds.