The generator matrix
1 1 1 1 1 1 1 1 1 X 1 1 1 X
0 X 0 0 0 0 0 0 0 0 0 X X X
0 0 X 0 0 0 0 0 0 0 X X X 0
0 0 0 X 0 0 0 0 0 0 X 0 X X
0 0 0 0 X 0 0 0 0 X 0 0 X X
0 0 0 0 0 X 0 0 0 X 0 X 0 X
0 0 0 0 0 0 X 0 0 X 0 X X 0
0 0 0 0 0 0 0 X 0 X X 0 X 0
0 0 0 0 0 0 0 0 X X X 0 0 X
generates a code of length 14 over Z2[X]/(X^2) who´s minimum homogenous weight is 8.
Homogenous weight enumerator: w(x)=1x^0+77x^8+296x^12+256x^14+331x^16+56x^20+7x^24
The gray image is a linear code over GF(2) with n=28, k=10 and d=8.
This code was found by Heurico 1.16 in 0.0112 seconds.