The generator matrix

 1  0  0  0  0  1  1  1 X^2+X  1  0  1  1  1  1 X^2+X  X  1 X^2+X  1  0 X^2+X  X X^2+X X^2+X  1  1  1  1 X^2+X  1  1  1 X^2+X  1
 0  1  0  0  0  0 X^2  0 X^2 X+1  1  1  1 X^2 X+1 X^2+X  1  X  X  1  1  0  1 X^2+X  1 X^2+1 X^2+X+1 X^2+X X+1  1 X^2 X^2+1 X+1  0  0
 0  0  1  0  0  0  1  1  1 X^2+1 X^2+X+1 X^2+X X+1  X X^2+X  X  1 X^2+X+1  1 X^2 X^2+1  1 X^2+X  0  0 X+1  0 X^2+X+1 X^2+X  1 X^2+X+1 X^2+X  1  1 X^2+X
 0  0  0  1  0  1  1  X X^2+X+1 X^2  1 X^2+X X^2+X+1 X^2+1 X^2+X  1  1 X^2  X X^2+X+1 X^2 X+1 X^2+1  1 X^2 X^2+1 X+1 X^2 X^2+X+1 X^2 X+1 X^2+X X^2+X  0  0
 0  0  0  0  1  1  X X+1 X+1 X^2+1  X X+1 X^2+X+1 X^2 X^2+X X^2+1 X^2+X+1 X^2 X^2+X+1  1  X  0  0  0 X^2+X+1  0 X^2 X^2+X  0 X^2+1  0  X  X X^2+X+1 X+1
 0  0  0  0  0 X^2  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2  0  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+144x^27+666x^28+1316x^29+2309x^30+3588x^31+5180x^32+6730x^33+8115x^34+8998x^35+8350x^36+7150x^37+5336x^38+3546x^39+2176x^40+1030x^41+548x^42+234x^43+72x^44+30x^45+11x^46+2x^47+3x^48+1x^50

The gray image is a linear code over GF(2) with n=140, k=16 and d=54.
This code was found by Heurico 1.13 in 22.8 seconds.