The generator matrix

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

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+18x^22+42x^23+33x^24+42x^25+32x^26+14x^27+18x^28+16x^29+18x^30+6x^31+4x^32+2x^33+4x^34+2x^35+4x^37

The gray image is a linear code over GF(2) with n=52, k=8 and d=22.
This code was found by Heurico 1.10 in 0 seconds.