The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+154x^61+186x^62+282x^63+330x^64+236x^65+276x^66+208x^67+192x^68+134x^69+34x^70+6x^71+2x^72+2x^73+3x^80+2x^89

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 0.297 seconds.