The generator matrix

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

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+55x^8+206x^10+430x^12+646x^14+477x^16+170x^18+58x^20+2x^22+3x^24

The gray image is a linear code over GF(2) with n=28, k=11 and d=8.
As d=8 is an upper bound for linear (28,11,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 11.
This code was found by Heurico 1.16 in 0.0338 seconds.