The generator matrix

1 0 0 0 0 0 1 1 1 X 1 1 0 1 1 X 1 1 X 1 1 0 X 1 1 1
0 1 0 0 0 0 0 0 0 0 0 1 X 1 1 1 1 X+1 X X+1 X 1 1 1 1 0
0 0 1 0 0 0 0 1 1 1 0 1 1 X X+1 X+1 1 X+1 1 X 0 1 0 1 X+1 0
0 0 0 1 0 0 0 1 X X+1 1 X+1 1 X X X+1 X 0 X X 1 X+1 1 X 1 0
0 0 0 0 1 0 1 0 1 X+1 X+1 0 X+1 X X+1 X X+1 X X 0 X+1 1 0 0 X+1 0
0 0 0 0 0 1 1 X+1 0 1 X X 0 0 X+1 X+1 X X 1 1 1 1 0 1 X+1 1
0 0 0 0 0 0 X X 0 0 0 0 X X 0 X X 0 0 X X 0 X X X 0

generates a code of length 26 over Z2[X]/(X^2) who´s minimum homogenous weight is 17.

Homogenous weight enumerator: w(x)=1x^0+22x^17+97x^18+192x^19+288x^20+356x^21+472x^22+584x^23+758x^24+832x^25+814x^26+912x^27+830x^28+708x^29+512x^30+328x^31+217x^32+122x^33+81x^34+32x^35+18x^36+8x^37+8x^38

The gray image is a linear code over GF(2) with n=52, k=13 and d=17.
This code was found by Heurico 1.10 in 0.735 seconds.