The generator matrix

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

generates a code of length 64 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 59.

Homogenous weight enumerator: w(x)=1x^0+96x^59+625x^60+880x^61+1196x^62+1066x^63+1222x^64+716x^65+911x^66+480x^67+445x^68+220x^69+166x^70+102x^71+33x^72+24x^73+7x^74+2x^76

The gray image is a code over GF(2) with n=512, k=13 and d=236.
This code was found by Heurico 1.16 in 0.688 seconds.