The generator matrix

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

generates a code of length 13 over Z2[X]/(X^2) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+303x^8+464x^10+1336x^12+1120x^14+639x^16+208x^18+24x^20+1x^24

The gray image is a linear code over GF(2) with n=26, k=12 and d=8.
As d=8 is an upper bound for linear (26,12,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 12.
This code was found by Heurico 1.16 in 1.26 seconds.