The generator matrix

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

generates a code of length 34 over Z2[X]/(X^3) who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+116x^30+305x^32+266x^34+184x^36+118x^38+20x^40+6x^42+6x^46+2x^48

The gray image is a linear code over GF(2) with n=136, k=10 and d=60.
This code was found by Heurico 1.16 in 0.0444 seconds.