The generator matrix

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

generates a code of length 14 over Z2[X]/(X^2) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+6x^12+8x^13+4x^14+8x^15+1x^16+3x^18+1x^26

The gray image is a linear code over GF(2) with n=28, k=5 and d=12.
This code was found by Heurico 1.16 in 0.000424 seconds.