The generator matrix

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

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+144x^26+543x^28+8x^29+854x^30+176x^31+1665x^32+1016x^33+2867x^34+1696x^35+3044x^36+1016x^37+1690x^38+176x^39+859x^40+8x^41+428x^42+149x^44+32x^46+10x^48+1x^50+1x^56

The gray image is a linear code over GF(2) with n=140, k=14 and d=52.
This code was found by Heurico 1.16 in 8.42 seconds.