The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X X^2 X 0 0 1 X^2 1 X 1 0 1 X^2 0 X X
0 X 0 0 0 0 0 X^2 X^2 X X^2+X X X X X^2+X X 0 X^2+X 0 X X^2 X^2+X X X^2 X^2+X X X^2+X X X^2+X 0 X^2+X X X^2 X 0
0 0 X 0 0 X^2 X^2+X X X X X X X^2+X 0 0 0 X^2 X^2 0 X X X X^2 X^2 X 0 X^2 X^2+X X X X^2 X 0 X 0
0 0 0 X 0 X^2+X X^2+X X X^2 X^2+X X^2+X 0 0 X X X^2 X X^2 X X^2 0 X^2 X^2+X X 0 X^2 X^2 X^2+X X X^2 X^2+X X^2+X X X^2 0
0 0 0 0 X X X^2 X^2+X X X^2+X X^2 X^2 X X^2 X^2+X X X X^2 X 0 X X X^2+X X^2 0 X^2 X^2+X X^2 0 0 X X 0 X^2+X X
generates a code of length 35 over Z2[X]/(X^3) who´s minimum homogenous weight is 29.
Homogenous weight enumerator: w(x)=1x^0+52x^29+121x^30+178x^31+151x^32+210x^33+262x^34+206x^35+229x^36+172x^37+137x^38+118x^39+90x^40+50x^41+20x^42+26x^43+9x^44+12x^45+4x^46
The gray image is a linear code over GF(2) with n=140, k=11 and d=58.
This code was found by Heurico 1.16 in 0.145 seconds.