The generator matrix

 1  0  1  1  1  0  1  1  0  1  1  1  1  1
 0  1  1  0  1  1  0  1  1  0  0  0  0  0
 0  0  X  0  0  0  0  0  0  0  0  X  0  X
 0  0  0  X  0  0  0  0  0  0  0  X  X  X
 0  0  0  0  X  0  0  0  0  0  X  0  X  X
 0  0  0  0  0  X  0  0  0  0  X  0  0  X
 0  0  0  0  0  0  X  0  0  0  X  0  X  0
 0  0  0  0  0  0  0  X  0  0  X  X  0  X
 0  0  0  0  0  0  0  0  X  0  0  X  X  0
 0  0  0  0  0  0  0  0  0  X  X  X  X  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+32x^6+109x^8+224x^10+256x^11+392x^12+768x^13+512x^14+768x^15+427x^16+256x^17+224x^18+88x^20+32x^22+7x^24

The gray image is a linear code over GF(2) with n=28, k=12 and d=6.
This code was found by Heurico 1.16 in 0.0605 seconds.