The generator matrix

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

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+68x^59+288x^60+450x^61+524x^62+494x^63+606x^64+468x^65+490x^66+304x^67+202x^68+100x^69+53x^70+24x^71+4x^73+2x^74+4x^75+6x^76+2x^77+2x^78+2x^79+1x^80+1x^86

The gray image is a code over GF(2) with n=512, k=12 and d=236.
This code was found by Heurico 1.16 in 0.421 seconds.