The generator matrix

 1  0  0  1  1  1  0 X^2+2 X^2+2 X^2+2  1  1  1  1  X  1  1 X+2  1  1 X^2+X  1  1  1 X^2+X+2 X^2+X+2 X+2  1  1  1  X  X  1  1 X^2+X X^2  1  1  1  2  1  1 X^2+2  X  X  2  1 X+2  2  2  1  1  0 X^2+X  1 X^2+X+2  1  1  1  1  1  1  0 X^2+2
 0  1  0  0 X^2+3 X^2+1  1  X  1  1  1  1 X^2 X^2+2 X^2+X+2  X X+1  1 X+1  X  1 X^2+X+1 X^2+X+1 X+2  0  1  1 X^2+2 X+2  3  0  1 X+1  2  1  1 X^2+X+2 X+2 X+3  1  2  0  1  1  1 X^2+X X^2+3  1  1 X^2+2 X^2+1  3  1  1 X^2+2  1 X^2+X X^2+1 X^2+1 X+2 X^2+X+3 X^2+X+1  1 X^2+X+2
 0  0  1 X+1 X+3  2 X^2+X+1  1  X  3  1 X^2+X X^2+X+2  3  1 X+2 X^2 X^2+X X+3  1  3 X^2+X  1  2  1  0 X^2+X+3 X+3 X^2+1 X^2+X  1 X^2+1 X^2+X+3 X^2+X+2 X^2  3 X+3 X^2 X^2+X+2 X^2+X X^2+1 X^2+2 X+3 X+2  2  1 X^2+X+1  3 X^2  1  1 X^2+2  X X^2+X+1 X+1 X^2+X+1 X^2  3  0 X^2+X+2 X+3 X^2+2 X^2+X+3  1
 0  0  0 X^2 X^2  0 X^2 X^2+2 X^2  2  0 X^2 X^2  0 X^2+2  0 X^2  0  0 X^2 X^2+2  0 X^2+2 X^2+2  0 X^2  2  2  2  2  2  0 X^2+2  2  2 X^2 X^2+2  0 X^2+2 X^2+2 X^2 X^2+2  0  2 X^2+2  0  2 X^2 X^2 X^2 X^2+2 X^2  2  0 X^2+2 X^2+2 X^2  2 X^2+2  2  0  2 X^2+2 X^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+568x^59+995x^60+1820x^61+1906x^62+2242x^63+2125x^64+2022x^65+1423x^66+1460x^67+860x^68+514x^69+199x^70+174x^71+34x^72+16x^73+5x^74+4x^75+1x^76+10x^77+3x^78+2x^81

The gray image is a code over GF(2) with n=512, k=14 and d=236.
This code was found by Heurico 1.16 in 816 seconds.