The generator matrix
1 0 0 1 1 1 X^2+X 1 1 X X^2 1 0 1 1 X^2+X 1 0 1 1 X X X^2 1 1 1
0 1 0 1 0 1 1 X X 1 1 X+1 0 X+1 X^2+1 1 X X X^2 X^2 1 1 1 X^2+X X+1 0
0 0 1 1 1 0 1 X+1 X X^2+X X^2+X+1 X 1 X+1 X 1 X^2+X 1 X+1 1 1 X X^2+X+1 X^2 0 0
0 0 0 X 0 0 0 0 0 0 0 X^2 X X X^2+X X X^2+X X^2 X^2+X X X^2 X X^2+X X X^2+X 0
0 0 0 0 X 0 0 0 X X X X^2+X X^2 X^2 0 X X X X^2 0 X^2+X 0 X^2+X 0 X^2 0
0 0 0 0 0 X X^2+X X^2+X X X^2+X X^2 0 X X^2+X X^2 X X^2 X^2 X X^2 X X^2 X^2 X^2+X X 0
generates a code of length 26 over Z2[X]/(X^3) who´s minimum homogenous weight is 18.
Homogenous weight enumerator: w(x)=1x^0+72x^18+146x^19+427x^20+824x^21+1587x^22+2418x^23+3583x^24+4844x^25+4976x^26+4648x^27+3755x^28+2608x^29+1500x^30+772x^31+376x^32+108x^33+84x^34+14x^35+18x^36+5x^38+2x^39
The gray image is a linear code over GF(2) with n=104, k=15 and d=36.
This code was found by Heurico 1.16 in 11.1 seconds.