The generator matrix

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

generates a code of length 34 over Z2[X]/(X^3) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+53x^32+64x^33+80x^34+40x^36+16x^40+2x^48

The gray image is a linear code over GF(2) with n=136, k=8 and d=64.
This code was found by Heurico 1.16 in 0.0118 seconds.