The generator matrix

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

generates a code of length 14 over Z2[X]/(X^2) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+32x^6+16x^7+141x^8+144x^9+416x^10+624x^11+872x^12+1264x^13+1152x^14+1264x^15+907x^16+624x^17+416x^18+144x^19+120x^20+16x^21+32x^22+7x^24

The gray image is a linear code over GF(2) with n=28, k=13 and d=6.
This code was found by Heurico 1.16 in 0.213 seconds.