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 X X 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
0 2X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2X 0 0 2X 2X 0 2X 0 2X 2X 2X 0 2X 0 2X 2X 2X 2X 2X 2X 2X 2X 2X 0 2X 0 2X 2X 2X 0 2X 0 2X 2X 2X 2X 2X 0 0 2X 0 2X 2X 0 2X 2X 0 0
0 0 2X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2X 0 2X 2X 0 0 2X 0 2X 0 2X 2X 2X 0 2X 0 2X 2X 2X 2X 2X 2X 2X 2X 2X 0 2X 0 2X 2X 2X 0 2X 0 2X 2X 2X 2X 2X 2X 0 2X 0 0 2X 2X 2X 2X 0
0 0 0 2X 0 0 0 0 0 0 0 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 0 2X 0 2X 2X 2X 2X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2X 2X 0 0 2X 2X 2X 2X 0 0 2X 2X 2X 2X 2X 2X 0 0 2X 2X 0 2X 2X 0 0
0 0 0 0 2X 0 0 0 2X 2X 2X 2X 2X 0 2X 2X 0 0 0 0 0 0 0 0 0 0 0 0 2X 2X 2X 2X 2X 2X 0 2X 0 2X 0 2X 0 2X 2X 2X 2X 0 2X 0 2X 2X 0 2X 2X 0 2X 0 2X 2X 2X 2X 2X 2X 0 2X 0 2X 0
0 0 0 0 0 2X 0 2X 2X 2X 0 0 0 0 2X 2X 2X 2X 0 0 0 0 0 0 2X 2X 2X 2X 2X 2X 0 0 0 0 0 2X 0 2X 2X 0 2X 0 2X 0 2X 2X 0 2X 0 2X 2X 2X 0 2X 2X 0 2X 0 2X 2X 2X 0 2X 2X 0 0 0
0 0 0 0 0 0 2X 2X 0 2X 2X 0 2X 2X 2X 0 0 2X 0 0 2X 2X 2X 2X 2X 2X 0 0 0 2X 0 0 2X 2X 0 0 2X 2X 2X 2X 0 0 0 2X 2X 0 0 2X 2X 2X 0 0 2X 0 2X 2X 2X 0 2X 0 0 0 2X 0 0 0 0
generates a code of length 67 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 64.
Homogenous weight enumerator: w(x)=1x^0+23x^64+32x^65+47x^66+832x^67+32x^68+32x^69+16x^70+8x^72+1x^130
The gray image is a code over GF(2) with n=536, k=10 and d=256.
This code was found by Heurico 1.16 in 0.203 seconds.