The generator matrix

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

generates a code of length 13 over Z2[X]/(X^2) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+150x^6+719x^8+2544x^10+4808x^12+4716x^14+2559x^16+768x^18+104x^20+14x^22+1x^24

The gray image is a linear code over GF(2) with n=26, k=14 and d=6.
As d=6 is an upper bound for linear (26,14,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 14.
This code was found by Heurico 1.16 in 2.55 seconds.