The generator matrix

 1  0  0  0  0  0  1  1  1  1  1  0  1  1
 0  1  0  0  0  0  0  0 X+1  X  1  1  0  0
 0  0  1  0  0  0  0  1  0 X+1  1  X  0  0
 0  0  0  1  0  0  1  1 X+1  0  1 X+1  0  0
 0  0  0  0  1  0  1  0  X  0  1  1  0  0
 0  0  0  0  0  1  1  0  1  1  X  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  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+101x^6+517x^8+1592x^10+3692x^12+4602x^14+3615x^16+1680x^18+484x^20+89x^22+11x^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 1.67 seconds.