The generator matrix

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

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+90x^66+634x^67+1307x^68+2092x^69+2940x^70+3680x^71+4041x^72+3830x^73+4150x^74+3402x^75+2470x^76+1828x^77+1161x^78+540x^79+253x^80+186x^81+74x^82+48x^83+15x^84+14x^85+9x^86+1x^88+2x^93

The gray image is a code over GF(2) with n=584, k=15 and d=264.
This code was found by Heurico 1.16 in 12 seconds.