The generator matrix

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

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+42x^20+62x^21+88x^22+98x^23+79x^24+98x^25+98x^26+110x^27+94x^28+82x^29+54x^30+46x^31+39x^32+14x^33+14x^34+2x^35+2x^38+1x^40

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 0.0415 seconds.