The generator matrix

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

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+116x^58+1168x^59+2340x^60+4066x^61+5482x^62+7300x^63+7804x^64+8984x^65+8160x^66+7634x^67+5202x^68+3594x^69+1931x^70+1136x^71+361x^72+124x^73+66x^74+42x^75+20x^76+5x^78

The gray image is a code over GF(2) with n=520, k=16 and d=232.
This code was found by Heurico 1.16 in 36 seconds.