The generator matrix

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

generates a code of length 14 over Z2[X]/(X^2) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+262x^8+740x^10+1824x^12+2500x^14+1901x^16+716x^18+232x^20+12x^22+4x^24

The gray image is a linear code over GF(2) with n=28, k=13 and d=8.
As d=8 is an upper bound for linear (28,13,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 13.
This code was found by Heurico 1.16 in 0.572 seconds.