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 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 2X 2X 0 0 2X 2X 2X 2X 0 2X 0 2X 2X 2X 0 2X 2X 0 2X 2X 0 0 2X 2X 2X 2X 0 0 2X 2X 2X 2X 0 0 2X 0 0 2X 2X 2X 2X 2X 2X 2X 0 0 0 0
0 0 2X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2X 0 2X 2X 2X 2X 2X 2X 0 0 2X 2X 2X 2X 0 0 2X 2X 0 2X 2X 0 2X 2X 2X 2X 0 0 2X 2X 2X 2X 0 0 2X 2X 2X 2X 2X 2X 2X 2X 0 0 0 0 0 0 0 0
0 0 0 2X 0 0 0 0 0 0 0 2X 2X 2X 2X 2X 2X 2X 2X 2X 0 2X 2X 0 0 2X 2X 0 2X 0 2X 0 2X 2X 2X 0 0 2X 0 0 2X 0 2X 2X 2X 0 0 0 0 2X 2X 0 2X 0 0 0 0 2X 2X 2X 2X 2X 0 0 0 0 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 0 2X 0 2X 2X 2X 2X 0 2X 2X 0 2X 2X 2X 2X 0 0 2X 2X 2X 2X 0 2X 0 2X 0 2X 2X 0 2X 2X 2X 0 2X 2X 0 0 0 0 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 0 0 0 0 2X 2X 2X 2X 0 0 2X 2X 0 2X 2X 0 0 2X 0 2X 2X 2X 0 2X 0 2X 2X 2X 0 2X 0 0 2X 0 2X 2X 2X 2X 2X 2X 0 0 0 0
0 0 0 0 0 0 2X 2X 0 2X 2X 0 2X 2X 2X 0 0 2X 0 0 0 0 2X 2X 2X 2X 2X 2X 2X 0 0 2X 2X 0 0 2X 0 2X 0 2X 2X 2X 0 0 2X 0 0 0 0 2X 0 0 0 0 2X 2X 2X 2X 2X 0 0 2X 2X 2X 0 0 0 0
generates a code of length 68 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 64.
Homogenous weight enumerator: w(x)=1x^0+63x^64+896x^68+63x^72+1x^136
The gray image is a code over GF(2) with n=544, k=10 and d=256.
This code was found by Heurico 1.16 in 0.219 seconds.