The generator matrix

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

generates a code of length 65 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+867x^58+1956x^59+5130x^60+6576x^61+11745x^62+12652x^63+18773x^64+15860x^65+18683x^66+13412x^67+11713x^68+5768x^69+4564x^70+1876x^71+997x^72+244x^73+198x^74+24x^75+25x^76+6x^78+1x^80+1x^86

The gray image is a code over GF(2) with n=520, k=17 and d=232.
This code was found by Heurico 1.16 in 278 seconds.