The generator matrix
1 0 0 0 1 1 1 1 0 1 1 X 1 1 1 1
0 1 0 0 1 0 0 X+1 1 X 0 X 0 X+1 X+1 X
0 0 1 0 1 0 1 0 X+1 X 1 1 X+1 1 0 0
0 0 0 1 1 1 0 X X+1 X+1 1 X+1 0 X+1 0 1
0 0 0 0 X 0 0 0 X 0 X X 0 0 X 0
0 0 0 0 0 X 0 0 0 X X X X 0 0 0
0 0 0 0 0 0 X X X X 0 0 X 0 X 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+51x^10+60x^11+120x^12+188x^13+206x^14+224x^15+265x^16+344x^17+220x^18+156x^19+112x^20+44x^21+34x^22+8x^23+14x^24+1x^26
The gray image is a linear code over GF(2) with n=32, k=11 and d=10.
This code was found by Heurico 1.16 in 0.049 seconds.