The generator matrix

 1  0  0  0  1  1  1  0  1  1  X  1  1  1
 0  1  0  0  0  1  1  1  0  0  0  X  0  0
 0  0  1  0  1  1  0  1  0  1  1  X  0  0
 0  0  0  1  1  0  1  1  1  0  1  0  0  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  X  0  X
 0  0  0  0  0  0  X  0  0  0  X  X  X  0
 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  0  X  X
 0  0  0  0  0  0  0  0  0  X  X  0  0  X

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+66x^6+311x^8+304x^9+896x^10+1088x^11+1736x^12+2864x^13+2164x^14+2304x^15+1743x^16+1424x^17+912x^18+192x^19+296x^20+16x^21+58x^22+9x^24

The gray image is a linear code over GF(2) with n=28, k=14 and d=6.
This code was found by Heurico 1.16 in 3.91 seconds.