The generator matrix

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

generates a code of length 73 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 65.

Homogenous weight enumerator: w(x)=1x^0+226x^65+1306x^66+2938x^67+4819x^68+7504x^69+10386x^70+13470x^71+16166x^72+17026x^73+16376x^74+14244x^75+10878x^76+7200x^77+4168x^78+2334x^79+1147x^80+462x^81+232x^82+102x^83+43x^84+26x^85+10x^86+2x^88+2x^89+2x^90+2x^93

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 160 seconds.