The generator matrix
1 0 1 1 1 0 1 1 0 1 1 0 X 1
0 1 1 0 1 1 0 1 1 0 X+1 1 0 0
0 0 X 0 0 0 0 0 0 X 0 X X 0
0 0 0 X 0 0 0 0 0 X X X 0 0
0 0 0 0 X 0 0 0 X X X 0 0 0
0 0 0 0 0 X 0 0 X 0 X 0 X 0
0 0 0 0 0 0 X 0 X X X X X 0
0 0 0 0 0 0 0 X X X 0 0 X 0
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+46x^8+16x^9+49x^10+80x^11+108x^12+160x^13+108x^14+160x^15+89x^16+80x^17+86x^18+16x^19+12x^20+12x^22+1x^26
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 0.00707 seconds.