The generator matrix

1 0 0 0 0 0 0 1 1 1 0 1 1 1 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 1 0 0 X X 1 X+1 0 0
0 0 0 1 0 0 0 1 1 X 1 X+1 X+1 1 1 0
0 0 0 0 1 0 0 1 X X+1 X+1 1 X X+1 0 0
0 0 0 0 0 1 0 1 X+1 X X 0 1 1 1 0
0 0 0 0 0 0 1 X 1 X+1 1 0 1 0 X+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+129x^8+130x^9+412x^10+356x^11+940x^12+1220x^13+1641x^14+2388x^15+1999x^16+2440x^17+1524x^18+1068x^19+980x^20+540x^21+494x^22+28x^23+47x^24+22x^25+24x^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 1.10 in 0.579 seconds.