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

generates a code of length 64 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+56x^60+208x^61+71x^62+832x^63+47x^64+576x^65+16x^66+24x^68+176x^69+40x^70+1x^126

The gray image is a code over GF(2) with n=512, k=11 and d=240.
This code was found by Heurico 1.16 in 0.312 seconds.