The generator matrix
1 0 0 1 1 1 0 1 1 1 1 0 X 0 1 0 X 1 1 1 0 1 1 0 1 1
0 1 0 1 0 1 1 0 0 1 X+1 1 1 0 1 1 1 1 X X 0 X+1 X+1 X 0 0
0 0 1 1 1 0 1 0 1 X+1 X 0 1 1 1 0 X X+1 X 1 1 0 1 1 0 0
0 0 0 X 0 0 0 0 0 X 0 X X X 0 0 X X 0 0 X X X 0 X X
0 0 0 0 X 0 0 0 0 0 0 X X X X 0 X X X X 0 X 0 0 X 0
0 0 0 0 0 X 0 0 0 0 X X X X 0 X 0 X 0 X 0 0 0 X X X
0 0 0 0 0 0 X 0 0 0 0 0 X 0 X X X X 0 0 0 0 X X X X
0 0 0 0 0 0 0 X 0 X X X 0 0 X X 0 X X 0 0 X X X X X
0 0 0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 X X X X X X X 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+85x^18+266x^20+483x^22+765x^24+902x^26+757x^28+506x^30+241x^32+69x^34+16x^36+3x^38+1x^40+1x^44
The gray image is a linear code over GF(2) with n=52, k=12 and d=18.
This code was found by Heurico 1.16 in 25.7 seconds.