The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+414x^59+1177x^60+2156x^61+3120x^62+3414x^63+4276x^64+4406x^65+3831x^66+3518x^67+2787x^68+1788x^69+1034x^70+406x^71+201x^72+122x^73+67x^74+24x^75+12x^76+8x^77+4x^78+2x^80

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 11.6 seconds.