The generator matrix

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

generates a code of length 65 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+608x^60+856x^61+1820x^62+1936x^63+2673x^64+1736x^65+2156x^66+1376x^67+1418x^68+776x^69+480x^70+208x^71+241x^72+24x^73+52x^74+17x^76+4x^78+1x^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 10.8 seconds.