The generator matrix

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

generates a code of length 26 over Z2[X]/(X^3) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+58x^20+32x^22+146x^24+256x^25+64x^26+256x^27+120x^28+32x^30+43x^32+14x^36+2x^40

The gray image is a linear code over GF(2) with n=104, k=10 and d=40.
This code was found by Heurico 1.16 in 0.0481 seconds.