The generator matrix

 1  0  0  1  1  1  X  1  1  0  0  X  X  1
 0  1  0  1  0 X+1  1  0  1  1  X  1  1  X
 0  0  1  1  1  0  1  0 X+1  X  1 X+1 X+1  1
 0  0  0  X  0  X  0  X  0  X  0  X  0  0
 0  0  0  0  X  0  0  X  X  0  X  X  0  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+7x^10+32x^11+46x^12+38x^13+31x^14+28x^15+27x^16+24x^17+9x^18+4x^19+6x^20+2x^21+1x^22

The gray image is a linear code over GF(2) with n=28, k=8 and d=10.
This code was found by Heurico 1.16 in 0.00139 seconds.