The generator matrix

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

generates a code of length 65 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 61.

Homogenous weight enumerator: w(x)=1x^0+282x^61+479x^62+592x^63+585x^64+656x^65+459x^66+304x^67+228x^68+210x^69+140x^70+96x^71+17x^72+36x^73+8x^74+1x^78+1x^82+1x^88

The gray image is a code over GF(2) with n=520, k=12 and d=244.
This code was found by Heurico 1.16 in 0.438 seconds.