The generator matrix

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

generates a code of length 65 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 59.

Homogenous weight enumerator: w(x)=1x^0+392x^59+1227x^60+2134x^61+3044x^62+3350x^63+4525x^64+4142x^65+4237x^66+3440x^67+2633x^68+1712x^69+971x^70+410x^71+316x^72+122x^73+59x^74+40x^75+10x^76+2x^77+1x^78

The gray image is a code over GF(2) with n=520, k=15 and d=236.
This code was found by Heurico 1.16 in 10.7 seconds.