The generator matrix

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

generates a code of length 73 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+204x^66+1454x^67+2766x^68+4434x^69+5617x^70+6546x^71+7694x^72+8378x^73+7564x^74+7264x^75+5442x^76+3826x^77+2161x^78+1234x^79+505x^80+222x^81+138x^82+30x^83+32x^84+20x^85+4x^86

The gray image is a code over GF(2) with n=584, k=16 and d=264.
This code was found by Heurico 1.16 in 41.7 seconds.