The generator matrix

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

generates a code of length 26 over Z2[X]/(X^2) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+170x^20+300x^22+371x^24+382x^26+377x^28+272x^30+132x^32+38x^34+5x^36

The gray image is a linear code over GF(2) with n=52, k=11 and d=20.
This code was found by Heurico 1.10 in 0.047 seconds.