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

generates a code of length 65 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+256x^62+1022x^64+512x^66+256x^70+1x^128

The gray image is a code over GF(2) with n=520, k=11 and d=248.
This code was found by Heurico 1.16 in 0.328 seconds.