The generator matrix

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

generates a code of length 26 over Z2[X]/(X^2) who´s minimum homogenous weight is 19.

Homogenous weight enumerator: w(x)=1x^0+94x^19+211x^20+222x^21+201x^22+320x^23+417x^24+370x^25+405x^26+400x^27+385x^28+354x^29+251x^30+200x^31+137x^32+78x^33+39x^34+10x^35+1x^48

The gray image is a linear code over GF(2) with n=52, k=12 and d=19.
This code was found by Heurico 1.10 in 81 seconds.