The generator matrix

 1  0  0  0  1  1  1 X^2  1  1  1  0  1  0  0  1  1 X^2 X^2+X X^2+X  1  1 X^2+X X^2 X^2 X^2  X  1  1 X^2+X  1 X^2  1  1  1
 0  1  0  0  0  1  1  1 X^2+1 X^2+X  X X^2+X X+1  1  1 X+1 X^2  X  1  X X+1  X  1  1  1  X  0  1  X  1 X^2+X  0  0 X^2+X  X
 0  0  1  0  1  1 X^2 X^2+1 X^2+X  X X^2+1  1 X^2+1 X^2+X+1  0 X^2 X^2+X+1  1 X+1  0 X^2+X  X X^2+X X+1 X^2  1  1 X^2+X+1 X^2+1  1 X^2  1 X^2+X  1 X+1
 0  0  0  1  1  0 X^2+1  1 X^2  1  X X+1 X^2+X+1  X  1 X^2 X^2+1 X^2+1 X^2+X+1  1  1 X^2+X+1  0 X^2  X X+1 X^2 X^2+X  1 X^2  0 X^2+1  X X^2 X+1
 0  0  0  0  X  0  0  X  0  0 X^2+X X^2+X  X X^2+X X^2+X  X  0 X^2 X^2  X X^2+X  0 X^2+X X^2 X^2  0  X X^2+X  X X^2 X^2+X X^2+X  0  X X^2+X
 0  0  0  0  0 X^2  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2  0 X^2 X^2 X^2  0  0 X^2  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+370x^28+584x^29+1349x^30+1752x^31+2683x^32+3160x^33+4330x^34+4220x^35+4120x^36+3540x^37+3009x^38+1552x^39+1198x^40+448x^41+285x^42+92x^43+42x^44+12x^45+18x^46+2x^48+1x^50

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 32.7 seconds.