The generator matrix

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

generates a code of length 64 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+65x^60+294x^61+204x^62+408x^63+256x^64+300x^65+164x^66+208x^67+57x^68+68x^69+13x^70+5x^72+1x^74+2x^77+1x^82+1x^94

The gray image is a code over GF(2) with n=512, k=11 and d=240.
This code was found by Heurico 1.16 in 0.266 seconds.