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

generates a code of length 35 over Z2[X]/(X^3) who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+82x^27+151x^28+190x^29+302x^30+404x^31+486x^32+786x^33+1162x^34+1134x^35+1013x^36+894x^37+557x^38+354x^39+271x^40+150x^41+114x^42+72x^43+28x^44+28x^45+8x^46+2x^47+2x^48+1x^54

The gray image is a linear code over GF(2) with n=140, k=13 and d=54.
This code was found by Heurico 1.16 in 2.44 seconds.