The generator matrix

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

generates a code of length 14 over Z2[X]/(X^2) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+10x^10+8x^11+18x^12+24x^13+14x^14+24x^15+7x^16+8x^17+6x^18+6x^20+2x^22

The gray image is a linear code over GF(2) with n=28, k=7 and d=10.
This code was found by Heurico 1.16 in 0.00111 seconds.