The generator matrix

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

generates a code of length 16 over Z2[X]/(X^2) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+30x^10+84x^11+136x^12+184x^13+182x^14+236x^15+289x^16+272x^17+266x^18+172x^19+80x^20+56x^21+34x^22+20x^23+6x^24

The gray image is a linear code over GF(2) with n=32, k=11 and d=10.
This code was found by Heurico 1.10 in 0.016 seconds.