The generator matrix

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

generates a code of length 65 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+168x^60+192x^61+534x^62+368x^63+575x^64+416x^65+692x^66+384x^67+384x^68+160x^69+142x^70+16x^71+49x^72+8x^74+3x^76+2x^80+1x^88+1x^92

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 1.28 seconds.