The generator matrix

 1  0  0  0  1  1  1  0  1  1  1  X X^2+X  1 X^2 X^2+X  1  1  1  1  1  X X^2+X  1 X^2  1  X  1  1 X^2+X  1  1  1  0 X^2+X
 0  1  0  0  0  1  1  1 X^2+X+1 X^2+1  X  1 X^2+X X^2  1 X^2 X^2+X  1 X^2+1  0 X+1  1  1 X^2 X^2+X X^2+1 X^2 X^2 X^2+X  0 X+1 X^2+X+1 X^2+1 X^2  1
 0  0  1  0  1  1  0  1 X^2+1 X^2+X  X X^2+1  1  1  0 X^2  1 X^2+X+1  X X^2+X X^2 X^2 X+1 X^2  1 X^2+X  X  1  0  1  1 X^2+X X^2+X+1  1  1
 0  0  0  1  1  0  1 X^2+1 X^2+X+1 X^2 X^2+X+1  0 X+1 X^2  1  1  1 X^2+1 X^2+1 X^2+X  0 X^2+X X^2+X+1  1 X^2+1 X+1  1  X X^2+X X^2+1 X^2 X^2 X^2+X+1 X+1  X
 0  0  0  0 X^2  0  0 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0
 0  0  0  0  0 X^2  0  0  0  0  0  0  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2
 0  0  0  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0 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+393x^28+508x^29+1406x^30+1660x^31+2936x^32+2980x^33+4454x^34+3876x^35+4527x^36+3300x^37+3046x^38+1572x^39+1234x^40+380x^41+362x^42+60x^43+55x^44+12x^46+5x^48+1x^52

The gray image is a linear code over GF(2) with n=140, k=15 and d=56.
This code was found by Heurico 1.16 in 25 seconds.