The generator matrix

 1  0  0  0  0  1  1  1  0  1  X  1  1  1  1  1  1  X  X  1  1  1  0  X  1  1
 0  1  0  0  0  0  0  X  X  1  1 X+1  1  X X+1 X+1  0  X  1  1  0  1  X  X  0  0
 0  0  1  0  0  X  1 X+1  1  0  1  1  1  0  X X+1  X  0  X  X X+1  1  X  X  1  0
 0  0  0  1  0 X+1  1  0  1  X X+1  1  0 X+1  1  X  X  1  1  X  1 X+1  1  1  0  0
 0  0  0  0  1  1  X  1  1 X+1  X  0 X+1  0  1  X X+1 X+1  0  X  0  0  0  1  1  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+24x^20+74x^21+110x^22+80x^23+93x^24+100x^25+90x^26+122x^27+65x^28+66x^29+74x^30+52x^31+38x^32+16x^33+14x^34+2x^35+3x^36

The gray image is a linear code over GF(2) with n=52, k=10 and d=20.
This code was found by Heurico 1.16 in 0.0404 seconds.