The generator matrix

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

generates a code of length 26 over Z2[X]/(X^2) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+117x^22+110x^24+106x^26+72x^28+54x^30+37x^32+10x^34+4x^36+1x^38

The gray image is a linear code over GF(2) with n=52, k=9 and d=22.
As d=22 is an upper bound for linear (52,9,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 9.
This code was found by Heurico 1.10 in 0.093 seconds.