The generator matrix
1 0 1 1 1 0 1 1 0 1 1 0 0 X 1 1 1 1 1 1 0 0 1 1 1 1
0 1 1 0 1 1 0 1 1 X X+1 1 1 1 0 0 0 X+1 X+1 X+1 1 1 X+1 X+1 0 0
0 0 X 0 0 0 0 0 0 0 X 0 X X 0 X X 0 0 X 0 X X 0 X 0
0 0 0 X 0 0 0 0 0 X 0 0 X X 0 X 0 0 0 X X 0 X X 0 0
0 0 0 0 X 0 0 0 0 0 X X 0 X X 0 X 0 0 0 X 0 X X 0 0
0 0 0 0 0 X 0 0 0 0 0 X X X 0 0 0 X X X 0 X 0 X X 0
0 0 0 0 0 0 X 0 0 X 0 X X 0 X 0 0 X 0 X X 0 X 0 X X
0 0 0 0 0 0 0 X 0 0 X X X 0 X X 0 X X 0 X 0 0 0 0 X
0 0 0 0 0 0 0 0 X 0 0 0 0 0 X X X X 0 X 0 0 X X X 0
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+34x^18+16x^19+81x^20+80x^21+128x^22+176x^23+176x^24+240x^25+192x^26+240x^27+179x^28+176x^29+124x^30+80x^31+63x^32+16x^33+30x^34+11x^36+4x^38+1x^44
The gray image is a linear code over GF(2) with n=52, k=11 and d=18.
This code was found by Heurico 1.16 in 0.472 seconds.