The generator matrix

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

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+46x^11+79x^12+90x^13+116x^14+112x^15+131x^16+132x^17+104x^18+94x^19+72x^20+34x^21+4x^22+4x^23+4x^24+1x^28

The gray image is a linear code over GF(2) with n=32, k=10 and d=11.
This code was found by an older version of Heurico in 0 seconds.