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

generates a code of length 64 over Z4[X]/(X^2+2X+2) 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.