The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+58x^60+570x^61+821x^62+1474x^63+1037x^64+1200x^65+741x^66+766x^67+399x^68+572x^69+245x^70+172x^71+68x^72+42x^73+15x^74+4x^75+5x^76+2x^78

The gray image is a code over GF(2) with n=520, k=13 and d=240.
This code was found by Heurico 1.16 in 0.75 seconds.