The generator matrix

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

generates a code of length 35 over Z2[X]/(X^3) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+48x^26+72x^27+179x^28+258x^29+334x^30+436x^31+546x^32+776x^33+916x^34+1000x^35+956x^36+788x^37+611x^38+472x^39+309x^40+216x^41+122x^42+64x^43+49x^44+10x^45+14x^46+4x^47+7x^48+2x^50+1x^54+1x^56

The gray image is a linear code over GF(2) with n=140, k=13 and d=52.
This code was found by Heurico 1.16 in 2.16 seconds.