The generator matrix

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

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+31x^32+128x^33+30x^34+64x^37+2x^50

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 0.0119 seconds.