The generator matrix

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

generates a code of length 34 over Z2[X]/(X^3) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+114x^28+48x^29+344x^30+176x^31+737x^32+288x^33+742x^34+288x^35+692x^36+176x^37+302x^38+48x^39+102x^40+18x^42+16x^44+2x^46+2x^52

The gray image is a linear code over GF(2) with n=136, k=12 and d=56.
This code was found by Heurico 1.16 in 0.371 seconds.