The generator matrix

 1  0  1  1  1  0  1  1  0  1  1  0  X  1  1  1  1  0  1  1  1  0  1  0  0  X
 0  1  1  0  1  1  0  1  1  X X+1  1  1  0  0 X+1 X+1  1 X+1 X+1  0  1 X+1  1  1  X
 0  0  X  0  0  0  0  0  0  0  X  0  0  X  X  X  X  X  X  0  0  X  X  0  0  0
 0  0  0  X  0  0  0  0  0  X  0  0  0  0  X  X  0  X  X  X  X  X  X  X  X  0
 0  0  0  0  X  0  0  0  0  0  X  X  X  X  0  0  X  0  X  X  0  X  0  0  X  0
 0  0  0  0  0  X  0  0  X  0  0  X  0  X  X  0  X  X  X  X  X  0  X  0  X  0
 0  0  0  0  0  0  X  0  X  X  0  0  X  X  X  X  0  0  X  0  0  X  0  0  X  0
 0  0  0  0  0  0  0  X  X  0  X  0  X  X  0  X  X  X  0  X  0  0  0  0  0  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+100x^20+76x^22+274x^24+172x^26+188x^28+132x^30+59x^32+4x^34+16x^36+2x^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 0.0714 seconds.