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 2X  1  1  1  1  1  1  1  1  1  1
 0  X  0 X+2 2X 3X+2  0  X 2X+2 3X+2  2  X 2X+2 3X 2X+2 3X+2  0 X+2 2X+2 X+2 2X 3X+2 2X  X  0 3X  0 3X+2 3X  2 2X  X 2X  X 3X  2  2 3X+2  X 2X X+2  2  2 3X+2 3X  2  2  X 3X+2 3X+2 X+2  X  0  2 2X 2X+2  2 X+2 3X 3X+2  X  0  0  0  0
 0  0  2  0  0  2 2X+2 2X+2 2X+2 2X  2 2X 2X 2X+2 2X  2  0 2X+2 2X  0  2 2X+2 2X+2  0 2X  0 2X  2 2X  2 2X+2  2  2  2  0  2  0 2X 2X+2  0 2X+2 2X 2X+2 2X+2 2X  0 2X+2 2X  2  0 2X  2 2X 2X+2  0  2  0  0  2 2X 2X+2 2X  2 2X+2  0
 0  0  0  2 2X+2  2 2X+2  0  0  0 2X+2  2 2X+2  2  0  0 2X  0  2  0 2X  2  2  2 2X 2X+2  2 2X+2 2X  2 2X 2X 2X+2  2 2X 2X  0  2 2X  2 2X 2X 2X 2X+2 2X+2 2X+2 2X+2  0 2X 2X 2X  0  0  2  0  0  2 2X+2 2X+2 2X+2 2X+2 2X+2  2  0  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+64x^61+160x^62+64x^63+958x^64+544x^66+64x^69+128x^70+64x^71+1x^128

The gray image is a code over GF(2) with n=520, k=11 and d=244.
This code was found by Heurico 1.16 in 0.328 seconds.