The generator matrix

1 1 0 X 0 1 1 X X 1 X 0 X 0 1 1 1 X 1 0 X 1 0 1 1 1
X 0 1 1 1 X 0 1 X X+1 X 0 0 1 X+1 X+1 X X X 0 0 X+1 X 0 X+1 0
X+1 0 0 X+1 0 X X+1 X+1 0 X+1 X 1 1 1 0 0 X X 1 1 0 X 1 1 0 0
X+1 0 X+1 0 0 X+1 X X+1 0 1 1 1 0 0 X 1 X X 0 X 1 0 1 X+1 0 0
0 0 0 0 0 0 X X 1 X+1 1 X+1 1 X X 1 0 1 0 0 X X+1 0 1 1 0
0 0 0 0 0 0 X X X+1 1 X+1 X+1 1 X+1 X+1 X X+1 0 X+1 1 0 X+1 1 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+26x^18+84x^19+161x^20+208x^21+271x^22+322x^23+357x^24+410x^25+385x^26+414x^27+421x^28+334x^29+268x^30+190x^31+106x^32+70x^33+40x^34+14x^35+10x^36+2x^37+1x^38+1x^42

The gray image is a linear code over GF(2) with n=52, k=12 and d=18.
This code was found by an older version of Heurico in 0 seconds.