The generator matrix

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

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+108x^61+554x^62+764x^63+668x^64+550x^65+377x^66+360x^67+212x^68+196x^69+155x^70+52x^71+70x^72+18x^73+9x^74+1x^78+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 0.25 seconds.