The generator matrix

 1  0  0  0  0  0  1  1  1  X  0  X  0
 0  1  0  0  0  0  X  1  1  1  1  0  1
 0  0  1  0  0  0  0  0  X  X X+1  1 X+1
 0  0  0  1  0  0  1 X+1  0  1  1  X  1
 0  0  0  0  1  0  1  X  1  0 X+1  1  X
 0  0  0  0  0  1  1  0 X+1  1  X  0  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+215x^8+384x^9+160x^10+592x^12+1280x^13+704x^14+215x^16+384x^17+160x^18+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 0.298 seconds.