The generator matrix

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

generates a code of length 65 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+629x^60+952x^61+1762x^62+1904x^63+2280x^64+2140x^65+1982x^66+1664x^67+1350x^68+624x^69+620x^70+204x^71+137x^72+40x^73+54x^74+20x^75+11x^76+4x^77+6x^78

The gray image is a code over GF(2) with n=520, k=14 and d=240.
This code was found by Heurico 1.16 in 51.3 seconds.