The generator matrix

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

generates a code of length 14 over Z2[X]/(X^2) who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+12x^13+8x^14+7x^16+4x^17

The gray image is a linear code over GF(2) with n=28, k=5 and d=13.
This code was found by Heurico 1.16 in 0.00259 seconds.