The generator matrix
1 0 0 0 1 1 1 0 1 1 1 1 1 1 0 X
0 1 0 0 0 1 1 1 X X X+1 0 1 X+1 1 X
0 0 1 0 1 1 0 X+1 X 1 X+1 X 0 X+1 X+1 1
0 0 0 1 1 0 X+1 X+1 0 X X+1 1 X 1 1 X+1
0 0 0 0 X 0 X X X X 0 0 X X X 0
0 0 0 0 0 X 0 X 0 X 0 X X X 0 X
generates a code of length 16 over Z2[X]/(X^2) who´s minimum homogenous weight is 11.
Homogenous weight enumerator: w(x)=1x^0+30x^11+96x^12+114x^13+95x^14+112x^15+123x^16+116x^17+117x^18+110x^19+68x^20+26x^21+9x^22+4x^23+3x^26
The gray image is a linear code over GF(2) with n=32, k=10 and d=11.
This code was found by Heurico 1.16 in 0.0242 seconds.