The generator matrix

 1  0  0  0  0  0  1  1  1  1  0  1  1  1  X  1
 0  1  0  0  0  0  0  0  1  X  1  1  0  X  0  0
 0  0  1  0  0  0  0  0  1 X+1  X X+1  X  X  0  0
 0  0  0  1  0  0  0  1  1  1 X+1  X  0  1  0  0
 0  0  0  0  1  0  1  1  0  1  X  0 X+1  1  0  0
 0  0  0  0  0  1  1  0 X+1  1  1  0  0 X+1  X  0
 0  0  0  0  0  0  X  0  X  0  0  X  X  0  X  0
 0  0  0  0  0  0  0  X  0  0  0  X  X  X  0  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+164x^8+116x^9+348x^10+432x^11+1092x^12+1336x^13+1568x^14+2224x^15+1853x^16+2176x^17+1592x^18+1360x^19+996x^20+456x^21+448x^22+80x^23+118x^24+12x^25+12x^26

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 3.2 seconds.