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  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  X  1  X  1 X^2  1 X^2 X^2 X^2
 0 X^2+2  0  0  0 X^2 X^2+2 X^2  0  2 X^2 X^2+2  2 X^2+2  2 X^2+2  0 X^2+2  2 X^2 X^2+2  0 X^2  2  0 X^2  0  0 X^2+2 X^2+2 X^2+2  2  2  2 X^2 X^2 X^2  2 X^2+2  2  2 X^2+2  2 X^2+2  2 X^2 X^2+2  2 X^2+2  0 X^2 X^2+2  2  2  2  2  0 X^2+2  2 X^2 X^2+2 X^2 X^2 X^2 X^2
 0  0 X^2+2  0 X^2 X^2 X^2+2  0 X^2  2 X^2+2  0  0 X^2+2 X^2  2  2 X^2+2 X^2 X^2  2  2  2 X^2+2  0 X^2+2  2 X^2+2  0 X^2+2  2 X^2+2 X^2 X^2  0  0  0  2  2  0 X^2+2 X^2+2 X^2+2 X^2  2  0 X^2+2  0 X^2  2 X^2+2 X^2  0  0 X^2+2  2 X^2  0  2 X^2  2 X^2  2 X^2 X^2
 0  0  0 X^2+2 X^2  0 X^2+2 X^2 X^2+2  0  2 X^2+2 X^2 X^2  2  0 X^2  2 X^2 X^2  0  2 X^2  0  0 X^2+2 X^2+2 X^2+2  2  2 X^2+2  0  0  0 X^2+2  2 X^2+2  2  2 X^2+2 X^2  0 X^2 X^2+2  2  0  0 X^2+2 X^2+2  0  2  2  0  2 X^2 X^2+2 X^2 X^2 X^2+2 X^2+2  0 X^2 X^2  0  2
 0  0  0  0  2  0  0  0  0  2  2  2  2  2  2  2  2  2  0  0  0  0  2  2  2  2  0  2  2  0  0  0  0  2  2  0  0  2  2  0  2  0  0  0  0  0  2  2  2  0  0  0  0  2  2  2  2  0  0  2  2  2  2  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+169x^60+48x^61+224x^63+381x^64+480x^65+256x^66+224x^67+137x^68+48x^69+74x^72+5x^76+1x^116

The gray image is a code over GF(2) with n=520, k=11 and d=240.
This code was found by Heurico 1.16 in 2.34 seconds.