The generator matrix

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

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+66x^9+169x^10+250x^11+422x^12+638x^13+842x^14+1114x^15+1191x^16+1058x^17+916x^18+638x^19+410x^20+282x^21+118x^22+46x^23+24x^24+4x^25+3x^26

The gray image is a linear code over GF(2) with n=32, k=13 and d=9.
This code was found by Heurico 1.10 in 0.219 seconds.