The generator matrix

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

generates a code of length 73 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 65.

Homogenous weight enumerator: w(x)=1x^0+142x^65+1197x^66+2802x^67+4852x^68+7964x^69+10823x^70+13498x^71+15844x^72+16994x^73+15613x^74+14456x^75+10761x^76+7330x^77+4555x^78+2316x^79+1107x^80+432x^81+221x^82+90x^83+39x^84+18x^85+4x^86+4x^87+2x^88+3x^90+2x^95+2x^100

The gray image is a code over GF(2) with n=584, k=17 and d=260.
This code was found by Heurico 1.16 in 162 seconds.