The generator matrix

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

generates a code of length 16 over Z2[X]/(X^2) who´s minimum homogenous weight is 9.

Homogenous weight enumerator: w(x)=1x^0+60x^9+172x^10+270x^11+390x^12+638x^13+930x^14+1054x^15+1095x^16+1110x^17+954x^18+666x^19+410x^20+234x^21+118x^22+58x^23+24x^24+6x^25+2x^26

The gray image is a linear code over GF(2) with n=32, k=13 and d=9.
This code was found by Heurico 1.16 in 1.3 seconds.