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

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+64x^27+162x^28+228x^29+313x^30+412x^31+591x^32+794x^33+1018x^34+1056x^35+975x^36+878x^37+575x^38+396x^39+279x^40+198x^41+129x^42+56x^43+35x^44+14x^45+12x^46+5x^48+1x^50

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 67.4 seconds.