The generator matrix

 1  0  0  1  1  1 X^2  1  1  1  1 X^2+X  0  0  X  X  0  1  1  1 X^2+X  0  1  1  1 X^2+X  1  1  1  1  1  0  1 X^2  1
 0  1  0  1  X X^2+X+1  1  0 X^2+X X^2+1 X^2+X+1  1  1  X  1  1 X^2 X^2+X X^2+X X+1  1  1 X^2+1 X^2+1  0  0 X^2  1 X^2+X+1  X X^2+1  1 X+1  0  0
 0  0  1  1  1  0 X+1  X X^2+X+1 X+1  X  0 X+1  1 X^2 X+1  1 X+1  X  1  X  1 X^2+X X^2+1 X^2+X+1  1  1 X^2+1 X^2 X^2 X^2 X^2  0  X  0
 0  0  0  X  0 X^2+X  X X^2+X X^2+X X^2 X^2  0 X^2 X^2+X X^2+X X^2+X X^2+X  0  X  X X^2+X X^2 X^2+X  0  X  0 X^2 X^2+X  X  X X^2 X^2 X^2+X X^2  0
 0  0  0  0 X^2  0 X^2  0 X^2  0  0 X^2 X^2  0 X^2  0  0 X^2  0 X^2  0  0 X^2 X^2  0 X^2  0  0 X^2  0 X^2  0 X^2 X^2  0
 0  0  0  0  0 X^2  0  0  0  0 X^2 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0  0  0 X^2 X^2  0 X^2 X^2 X^2  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+49x^28+178x^29+367x^30+538x^31+661x^32+834x^33+1001x^34+970x^35+946x^36+950x^37+694x^38+446x^39+272x^40+134x^41+78x^42+30x^43+21x^44+16x^45+3x^46+2x^48+1x^50

The gray image is a linear code over GF(2) with n=140, k=13 and d=56.
This code was found by Heurico 1.16 in 1.43 seconds.