The generator matrix

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

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+156x^61+164x^62+392x^63+124x^64+368x^65+248x^66+304x^67+64x^68+172x^69+34x^70+8x^71+2x^72+8x^73+1x^78+1x^80+1x^94

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 0.203 seconds.