The generator matrix

 1  0  0  1  1  1 X^2+X  1  1  1  X  1  X X^2+X X^2  1  1  1  1  0  0 X^2+X  1  X  1  X  1  1  X  1  0  1  1  X  0
 0  1  0  1  0  1  1  X  1  X  1  1 X^2+X  1  1 X^2+1 X+1 X^2+X  0  X  1  X X^2+X+1  1 X^2  1 X+1  1  1 X+1 X^2 X^2 X^2+1  X  1
 0  0  1  1  1  0  1 X+1  1  X X^2+X X^2  1 X^2+1  1 X^2+1  0 X^2+1 X^2  1 X+1  1 X^2+X+1 X^2 X^2+X  X  1 X^2  0  1  1 X+1 X+1  1 X^2
 0  0  0  X  0  0  0  0  0  0  0  0 X^2 X^2  X  X X^2+X X^2+X X^2+X  X X^2+X  X X^2 X^2+X  X X^2+X  X X^2 X^2 X^2+X X^2  0 X^2  X  X
 0  0  0  0  X  0  0  0 X^2  X  X  X  X X^2+X  0 X^2+X  X X^2+X  X  X X^2+X X^2 X^2+X  0 X^2  X X^2+X  X  0 X^2+X X^2 X^2  X  X  0
 0  0  0  0  0  X X^2+X X^2+X  0  X X^2+X X^2 X^2+X  0 X^2+X X^2+X X^2  0  X  X X^2  0  X  0 X^2  X  0 X^2+X  X X^2 X^2+X  0  X X^2+X 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+84x^27+472x^28+560x^29+975x^30+1714x^31+2587x^32+3570x^33+4008x^34+4514x^35+4462x^36+3642x^37+2416x^38+1654x^39+1098x^40+534x^41+271x^42+98x^43+82x^44+14x^45+9x^46+2x^48+1x^58

The gray image is a linear code over GF(2) with n=140, k=15 and d=54.
This code was found by Heurico 1.16 in 23.5 seconds.