The generator matrix

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

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+291x^60+48x^61+524x^62+280x^63+809x^64+376x^65+758x^66+264x^67+350x^68+56x^69+208x^70+98x^72+14x^74+18x^76+1x^108

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 2.64 seconds.