The generator matrix

 1  0  0  0  1  1  1 X^2  1 X^2+X X^2  1 X^2+X  1  0  1  1  1  1  1  X X^2 X^2+X  1  0  1
 0  1  0  0  0  1  1  1 X^2+X+1  1  1 X^2+1  X X^2+X  1 X+1 X^2 X+1  1 X^2  1  1  X  X  X X^2
 0  0  1  0  1  1  X X+1  X X+1  X X+1  1  0 X^2+1 X^2  0  0 X+1  1 X+1 X^2+X  0 X^2+1  1 X^2
 0  0  0  1  1  0 X+1  1 X^2  0 X+1  1 X+1 X^2+1 X+1  1  0 X^2+X  0 X^2+1 X^2+X  X  1 X^2 X^2+X X^2+X
 0  0  0  0  X  0  0  0  0 X^2 X^2  0  X X^2 X^2+X X^2+X  X X^2+X  X X^2  X X^2+X  X X^2+X X^2 X^2
 0  0  0  0  0 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2  0 X^2  0 X^2 X^2

generates a code of length 26 over Z2[X]/(X^3) who´s minimum homogenous weight is 19.

Homogenous weight enumerator: w(x)=1x^0+80x^19+350x^20+858x^21+1607x^22+2482x^23+3946x^24+4166x^25+5533x^26+4464x^27+4093x^28+2416x^29+1537x^30+770x^31+313x^32+110x^33+27x^34+12x^35+2x^37+1x^44

The gray image is a linear code over GF(2) with n=104, k=15 and d=38.
This code was found by Heurico 1.16 in 10.8 seconds.