The generator matrix

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

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+649x^60+896x^61+1842x^62+1936x^63+2166x^64+2048x^65+2178x^66+1568x^67+1273x^68+800x^69+606x^70+144x^71+156x^72+32x^73+70x^74+5x^76+8x^78+5x^80+1x^84

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 13 seconds.