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.