The generator matrix

 1  0  1  1  1 3X+2  1  X  1 2X  1  1  2  1  1  1 X+2  1  1 2X+2  1 3X  1  1  1  1  1  1  0 X+2  1  1  1  1  1 2X 3X+2  1  1  1 2X  1  1  1  2 3X+2  1 3X  X  X 2X+2  1  1  1  1  1  1  X  0  1  1  1  1  X  0
 0  1 X+1 X+2 2X+3  1 2X+2  1 X+3  1 3X  1  1 2X X+1 3X+2  1 3X+3  2  1  X  1 X+1 3X+3  3 2X+1  3  0  1  1 3X+2 3X+1 2X+3  2 X+2  1  1 2X+3 2X+1  2  1 3X  2 X+2  1  1 3X+1  1  0  0  X 3X+2 2X  X 2X+1 2X+1 2X+2  1  1 3X+3 3X+3 3X+3 X+3 3X  1
 0  0  2  0 2X+2  2  0  2 2X+2 2X+2  0  2 2X+2  2 2X 2X+2  0 2X  2  0 2X+2  0 2X 2X  0 2X 2X  0  0  0 2X+2  2 2X+2  2 2X  2  2  0 2X+2 2X+2 2X 2X  0  2  2 2X  2  2  2 2X 2X+2 2X  2  2 2X  0 2X 2X 2X 2X  0  2 2X+2 2X  0
 0  0  0 2X  0  0  0  0 2X 2X 2X 2X 2X  0 2X 2X  0  0 2X 2X  0 2X 2X  0  0 2X 2X 2X  0  0 2X  0  0 2X  0  0 2X  0 2X  0 2X  0 2X  0  0 2X 2X 2X  0  0 2X 2X 2X 2X  0  0  0 2X  0 2X 2X 2X  0  0  0
 0  0  0  0 2X  0 2X 2X  0  0 2X 2X 2X 2X  0 2X 2X  0  0 2X  0  0 2X 2X  0 2X  0 2X 2X  0  0 2X  0 2X 2X  0 2X 2X  0  0  0  0  0 2X 2X 2X 2X  0  0 2X  0 2X 2X  0  0 2X 2X 2X 2X 2X 2X 2X  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+121x^60+334x^61+262x^62+654x^63+408x^64+702x^65+380x^66+500x^67+248x^68+320x^69+85x^70+30x^71+15x^72+14x^73+5x^74+2x^76+6x^77+1x^78+4x^80+3x^82+1x^84

The gray image is a code over GF(2) with n=520, k=12 and d=240.
This code was found by Heurico 1.16 in 0.437 seconds.