The generator matrix

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

generates a code of length 65 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+230x^64+576x^65+208x^66+8x^68+1x^128

The gray image is a code over GF(2) with n=520, k=10 and d=256.
This code was found by Heurico 1.16 in 6.25 seconds.