The generator matrix

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

generates a code of length 65 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+153x^58+1144x^59+2284x^60+3974x^61+5680x^62+7072x^63+8240x^64+8632x^65+8344x^66+7400x^67+5347x^68+3616x^69+2022x^70+992x^71+343x^72+152x^73+71x^74+24x^75+25x^76+10x^77+2x^78+8x^79

The gray image is a code over GF(2) with n=520, k=16 and d=232.
This code was found by Heurico 1.16 in 35.2 seconds.