The generator matrix

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

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+86x^19+259x^20+210x^21+112x^22+314x^23+546x^24+406x^25+186x^26+414x^27+564x^28+354x^29+191x^30+190x^31+157x^32+50x^33+22x^34+20x^35+9x^36+4x^37+1x^46

The gray image is a linear code over GF(2) with n=52, k=12 and d=19.
This code was found by Heurico 1.16 in 3.76 seconds.