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

generates a code of length 65 over Z4[X]/(X^2+2X+2) 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 6.22 seconds.