The generator matrix

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

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+56x^30+128x^31+191x^32+156x^33+48x^34+104x^35+164x^36+96x^37+30x^38+24x^39+10x^40+4x^41+6x^42+2x^46+2x^48+2x^50

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 0.0348 seconds.