The generator matrix

 1  0  0  0  1  1  1  1  0  1  X  1  1  1
 0  1  0  0  1  0  0  1  1  0  0  X  0  0
 0  0  1  0  1  0  1  0  1  1  1  X  0  0
 0  0  0  1  1  1  0  0  1  1 X+1  0  0  0
 0  0  0  0  X  0  0  0  0  0  X  X  0  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  0  X  0
 0  0  0  0  0  0  0  X  0  0  X  X  X  0
 0  0  0  0  0  0  0  0  X  X  0  X  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+55x^6+213x^8+128x^9+493x^10+640x^11+816x^12+1280x^13+942x^14+1280x^15+803x^16+640x^17+514x^18+128x^19+208x^20+43x^22+7x^24+1x^26

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 0.223 seconds.