The generator matrix

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

generates a code of length 14 over Z2[X]/(X^2) who´s minimum homogenous weight is 7.

Homogenous weight enumerator: w(x)=1x^0+68x^7+317x^8+464x^9+528x^10+1264x^11+2136x^12+2320x^13+2288x^14+2264x^15+1947x^16+1264x^17+752x^18+496x^19+200x^20+48x^21+16x^22+4x^23+7x^24

The gray image is a linear code over GF(2) with n=28, k=14 and d=7.
This code was found by Heurico 1.16 in 4.66 seconds.