The generator matrix
1 0 1 1 1 1 1 1
0 1 1 0 0 0 0 0
0 0 X 0 0 0 0 0
0 0 0 X 0 0 0 0
0 0 0 0 X 0 0 0
0 0 0 0 0 X 0 0
0 0 0 0 0 0 X 0
0 0 0 0 0 0 0 X
generates a code of length 8 over Z2[X]/(X^2) who´s minimum homogenous weight is 2.
Homogenous weight enumerator: w(x)=1x^0+12x^2+52x^4+116x^6+256x^7+150x^8+256x^9+116x^10+52x^12+12x^14+1x^16
The gray image is a linear code over GF(2) with n=16, k=10 and d=2.
This code was found by Heurico 1.16 in 0.00158 seconds.