The generator matrix

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

generates a code of length 13 over Z2[X]/(X^2) who´s minimum homogenous weight is 9.

Homogenous weight enumerator: w(x)=1x^0+34x^9+61x^10+68x^11+75x^12+52x^13+58x^14+72x^15+49x^16+26x^17+9x^18+4x^19+3x^20

The gray image is a linear code over GF(2) with n=26, k=9 and d=9.
As d=9 is an upper bound for linear (26,9,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 9.
This code was found by Heurico 1.10 in 0.016 seconds.