The generator matrix

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

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+79x^8+120x^10+336x^12+240x^14+207x^16+24x^18+16x^20+1x^24

The gray image is a linear code over GF(2) with n=26, k=10 and d=8.
As d=8 is an upper bound for linear (26,10,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 10.
This code was found by Heurico 1.16 in 0.00966 seconds.