The generator matrix

 1  0  1  1  1  0  1  1  0  1  1  0  1  1
 0  1  1  0  1  1  0  1  1  0 X+1  1  0  0
 0  0  X  0  0  0  0  0  0  0  0  X  X  X
 0  0  0  X  0  0  0  0  0  0  X  X  X  0
 0  0  0  0  X  0  0  0  0  0  X  0  X  X
 0  0  0  0  0  X  0  0  0  X  0  0  X  X
 0  0  0  0  0  0  X  0  0  X  0  X  0  X
 0  0  0  0  0  0  0  X  0  X  0  X  X  0
 0  0  0  0  0  0  0  0  X  X  X  0  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+85x^8+112x^10+544x^12+544x^14+579x^16+112x^18+64x^20+7x^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 0.0303 seconds.