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

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+56x^28+8x^30+105x^32+80x^34+512x^35+134x^36+40x^38+56x^40+25x^44+6x^48+1x^60

The gray image is a linear code over GF(2) with n=140, k=10 and d=56.
This code was found by Heurico 1.16 in 0.0578 seconds.