The generator matrix

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

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+46x^17+108x^18+130x^19+289x^20+392x^21+796x^22+1064x^23+1765x^24+2432x^25+2268x^26+2504x^27+1766x^28+1076x^29+844x^30+372x^31+249x^32+146x^33+72x^34+22x^35+25x^36+4x^37+8x^38+4x^39+1x^40

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 4.52 seconds.