The generator matrix

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

generates a code of length 64 over Z4[X]/(X^2+2) 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 0.282 seconds.