The generator matrix

 1  0  0  0  1  1  1  0  1  1  1  1  1  1  1  1  1  X  1  X  0  1  1  1  1  1
 0  1  0  0  0  1  1  1  X  X X+1  0  1 X+1  1  1 X+1  1  1  1  0 X+1 X+1 X+1  X  0
 0  0  1  0  1  1  0 X+1  X  0  X X+1  1  0  0 X+1  X  1 X+1 X+1  1 X+1 X+1 X+1  0  0
 0  0  0  1  1  0 X+1 X+1  0  1  X  0 X+1  X  1  X  0  1 X+1  1 X+1 X+1  0  X  X  0
 0  0  0  0  X  0  X  X  X  0  X  X  0  0  X  X  0  0  0  X  X  0  X  0  0  X
 0  0  0  0  0  X  0  X  0  X  X  X  0  0  X  0  X  X  X  0  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+33x^20+58x^21+93x^22+120x^23+97x^24+82x^25+90x^26+96x^27+69x^28+94x^29+86x^30+40x^31+22x^32+22x^33+18x^34+2x^36+1x^38

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 0.0396 seconds.