The generator matrix

1 0 0 0 0 0 1 1 1 0 1 1 X 0 1 1
0 1 0 0 0 0 0 1 1 X 0 X+1 X 1 0 0
0 0 1 0 0 0 1 0 X 1 X+1 X+1 1 0 1 0
0 0 0 1 0 0 1 X X+1 X X+1 X 0 1 X 0
0 0 0 0 1 0 1 X+1 0 1 X 0 X X+1 X 1
0 0 0 0 0 1 X 1 X 1 X+1 1 X+1 X+1 X X

generates a code of length 16 over Z2[X]/(X^2) who´s minimum homogenous weight is 9.

Homogenous weight enumerator: w(x)=1x^0+26x^9+74x^10+150x^11+227x^12+294x^13+405x^14+546x^15+628x^16+566x^17+425x^18+298x^19+217x^20+138x^21+55x^22+30x^23+15x^24+1x^26

The gray image is a linear code over GF(2) with n=32, k=12 and d=9.
This code was found by Heurico 1.10 in 0.078 seconds.