The generator matrix

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

generates a code of length 35 over Z2[X]/(X^3) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+122x^28+310x^30+40x^31+485x^32+264x^33+642x^34+432x^35+645x^36+240x^37+462x^38+40x^39+236x^40+8x^41+118x^42+40x^44+4x^46+6x^48+1x^52

The gray image is a linear code over GF(2) with n=140, k=12 and d=56.
This code was found by Heurico 1.16 in 0.529 seconds.