The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  1  X  1  1  X  1  1  X  X  X
 0  X  0  X  0 X^2  X X^2+X  0 X^2  X X^2+X  0  0 X^2+X  X X^2+X X^2 X^2  0 X^2 X^2+X  0 X^2+X  X  0
 0  0  X  X  0  X X^2+X X^2  0  X  X  0  0 X^2+X  X X^2  0  X X^2  X  0 X^2 X^2+X X^2 X^2+X X^2
 0  0  0 X^2  0  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2  0  0 X^2 X^2 X^2  0  0 X^2 X^2
 0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2 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 22.

Homogenous weight enumerator: w(x)=1x^0+44x^22+8x^23+108x^24+56x^25+115x^26+56x^27+62x^28+8x^29+26x^30+20x^32+7x^34+1x^40

The gray image is a linear code over GF(2) with n=104, k=9 and d=44.
This code was found by Heurico 1.16 in 0.0121 seconds.