The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  0  X  0 X^2 X^2  0  X  X  X  1  X  1  1  1
 0  X  0  0  0  0  0  0  0  X X^2+X  X  X X^2+X  X X^2  X X^2+X X^2  0 X^2 X^2 X^2+X  X  0  0  X  X X^2+X  X X^2+X X^2+X X^2  X  0
 0  0  X  0  0  0  X X^2+X  X  0  0  0  X  X X^2+X X^2  X  0 X^2+X X^2  X X^2 X^2 X^2+X  X  X  0  0 X^2+X X^2 X^2  X  X X^2 X^2
 0  0  0  X  0  X  X X^2+X  0  X  X X^2  0 X^2 X^2+X  X X^2+X X^2+X X^2+X X^2+X  X X^2  0 X^2  0 X^2+X X^2+X  X X^2+X  0 X^2+X  0 X^2 X^2  0
 0  0  0  0  X  X  0 X^2+X  X X^2 X^2+X X^2+X  0 X^2+X  X X^2  0  0 X^2 X^2+X X^2+X  X X^2 X^2+X X^2+X X^2  X X^2  0 X^2+X  0  0  0 X^2+X X^2
 0  0  0  0  0 X^2  0  0  0  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2  0  0 X^2  0 X^2 X^2  0  0 X^2  0
 0  0  0  0  0  0 X^2  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 X^2  0  0 X^2  0 X^2 X^2  0 X^2  0
 0  0  0  0  0  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2  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+160x^26+4x^27+514x^28+68x^29+924x^30+364x^31+1828x^32+948x^33+2719x^34+1316x^35+2698x^36+972x^37+1872x^38+356x^39+950x^40+60x^41+438x^42+8x^43+147x^44+28x^46+5x^48+3x^50+1x^60

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 8.32 seconds.