The generator matrix

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

generates a code of length 64 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+186x^57+1220x^58+2460x^59+3922x^60+5222x^61+7095x^62+8278x^63+8967x^64+8478x^65+7192x^66+5152x^67+3510x^68+1962x^69+1134x^70+438x^71+204x^72+72x^73+12x^74+8x^75+20x^76+3x^78

The gray image is a code over GF(2) with n=512, k=16 and d=228.
This code was found by Heurico 1.16 in 38.4 seconds.