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 X X X X X X X X 1 X 1 X X 1 X 1 X X X 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1
0 2X 0 0 0 0 0 0 0 2X 2X 2X 2X 2X 2X 2X 0 0 0 0 0 0 0 0 2X 2X 2X 2X 2X 2X 2X 2X 2X 0 2X 0 0 2X 0 2X 0 0 0 2X 2X 2X 2X 0 0 0 0 0 2X 2X 0 2X 2X 0 0 2X 2X 0 2X 2X
0 0 2X 0 0 0 2X 2X 2X 2X 2X 0 2X 2X 0 0 0 0 0 0 2X 2X 2X 2X 2X 2X 2X 2X 0 0 0 0 2X 0 2X 0 2X 0 2X 0 0 2X 2X 2X 2X 0 0 0 0 0 0 2X 2X 0 2X 2X 0 2X 2X 2X 2X 0 0 0
0 0 0 2X 0 2X 2X 2X 0 0 0 0 2X 2X 2X 2X 0 0 2X 2X 2X 2X 0 0 0 0 2X 2X 2X 2X 0 0 0 0 2X 2X 2X 2X 0 0 2X 2X 0 0 2X 2X 0 0 0 2X 2X 2X 0 2X 2X 2X 0 0 0 0 2X 0 2X 0
0 0 0 0 2X 2X 0 2X 2X 0 2X 2X 2X 0 0 2X 0 2X 2X 0 0 2X 2X 0 0 2X 2X 0 0 2X 2X 0 0 2X 2X 0 0 2X 2X 0 2X 2X 0 2X 0 0 2X 0 2X 2X 0 0 0 0 2X 2X 0 2X 0 2X 0 0 2X 2X
generates a code of length 64 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 64.
Homogenous weight enumerator: w(x)=1x^0+252x^64+2x^80+1x^96
The gray image is a code over GF(2) with n=512, k=8 and d=256.
This code was found by Heurico 1.16 in 0.14 seconds.