The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1
0 X 0 0 0 0 0 0 0 0 0 0 0 X 0 X X
0 0 X 0 0 0 0 0 0 0 0 0 X X X X X
0 0 0 X 0 0 0 0 0 0 0 0 X 0 0 X X
0 0 0 0 X 0 0 0 0 0 0 0 X X X 0 0
0 0 0 0 0 X 0 0 0 0 0 X X X 0 X X
0 0 0 0 0 0 X 0 0 0 0 X 0 0 0 X X
0 0 0 0 0 0 0 X 0 0 0 X 0 X X X X
0 0 0 0 0 0 0 0 X 0 0 X 0 X X 0 0
0 0 0 0 0 0 0 0 0 X 0 X X 0 X 0 0
0 0 0 0 0 0 0 0 0 0 X X X 0 X X X
generates a code of length 17 over Z2[X]/(X^2) who´s minimum homogenous weight is 8.
Homogenous weight enumerator: w(x)=1x^0+112x^8+364x^12+1774x^16+1024x^18+568x^20+224x^24+28x^28+1x^32
The gray image is a linear code over GF(2) with n=34, k=12 and d=8.
This code was found by Heurico 1.16 in 0.128 seconds.