The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 X X X 1 X 1 1
0 X 0 0 0 0 0 0 0 0 0 X 0 0 X X 0 0 X X X X X X 0 X
0 0 X 0 0 0 0 0 0 0 0 X X X X X 0 X X X 0 X 0 0 X X
0 0 0 X 0 0 0 0 0 0 X 0 X X 0 X X X X 0 X X 0 0 0 X
0 0 0 0 X 0 0 0 0 0 X 0 0 X X X X 0 0 X 0 X X X X 0
0 0 0 0 0 X 0 0 0 X 0 0 0 X X 0 X 0 X 0 0 X 0 X X X
0 0 0 0 0 0 X 0 0 X 0 0 X 0 0 X X 0 X 0 X 0 X X X 0
0 0 0 0 0 0 0 X 0 X X X X 0 0 0 0 0 X 0 0 X 0 X X 0
0 0 0 0 0 0 0 0 X X X X 0 0 X X X X X 0 0 X X 0 X X
generates a code of length 26 over Z2[X]/(X^2) who´s minimum homogenous weight is 18.
Homogenous weight enumerator: w(x)=1x^0+33x^18+66x^20+16x^21+64x^22+80x^23+64x^24+160x^25+67x^26+160x^27+64x^28+80x^29+60x^30+16x^31+47x^32+27x^34+14x^36+4x^38+1x^42
The gray image is a linear code over GF(2) with n=52, k=10 and d=18.
This code was found by Heurico 1.16 in 1.61 seconds.