The generator matrix

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

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+480x^28+1534x^32+1664x^36+384x^40+32x^44+1x^64

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 72.9 seconds.