The generator matrix

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

generates a code of length 26 over Z2[X]/(X^3) who´s minimum homogenous weight is 17.

Homogenous weight enumerator: w(x)=1x^0+8x^17+65x^18+76x^19+136x^20+516x^21+323x^22+1776x^23+853x^24+3744x^25+1323x^26+3784x^27+908x^28+1816x^29+290x^30+496x^31+129x^32+56x^33+43x^34+12x^35+20x^36+4x^37+3x^38+1x^40+1x^42

The gray image is a linear code over GF(2) with n=104, k=14 and d=34.
This code was found by Heurico 1.16 in 22.5 seconds.