The generator matrix

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

generates a code of length 16 over Z2[X]/(X^2) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+215x^8+216x^9+338x^10+284x^11+1000x^12+1428x^13+1717x^14+2172x^15+1703x^16+2212x^17+1596x^18+1268x^19+1048x^20+476x^21+418x^22+116x^23+129x^24+20x^25+26x^26+1x^30

The gray image is a linear code over GF(2) with n=32, k=14 and d=8.
This code was found by Heurico 1.16 in 3.69 seconds.