The generator matrix

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

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+96x^60+300x^61+211x^62+308x^63+221x^64+308x^65+202x^66+300x^67+96x^68+1x^72+1x^74+1x^82+1x^86+1x^88

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 0.203 seconds.