The generator matrix

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

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+290x^8+520x^10+1240x^12+1200x^14+613x^16+200x^18+32x^20

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 1.10 in 2.05 seconds.