The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  0  1  1  1  1  1  1  0  1  X  1  X  X  1  1
 0  X  0 X^2+X  0 X^2+X  0 X^2+X X^2 X^2+X  0 X^2+X  0 X^2+X X^2+X  0 X^2+X X^2  X  X X^2 X^2+X  X X^2+X  X  0  X  0 X^2+X X^2 X^2+X X^2+X X^2+X  0
 0  0 X^2  0  0  0  0  0 X^2  0  0  0 X^2  0 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2  0  0
 0  0  0 X^2  0  0  0 X^2  0  0  0 X^2  0 X^2 X^2 X^2  0 X^2  0  0  0  0 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2
 0  0  0  0 X^2  0  0  0  0 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0  0 X^2  0 X^2  0  0 X^2 X^2 X^2
 0  0  0  0  0 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2  0  0  0 X^2 X^2  0  0  0 X^2 X^2 X^2  0
 0  0  0  0  0  0 X^2  0 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2  0  0  0 X^2  0  0 X^2  0 X^2 X^2  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+35x^28+108x^30+224x^32+306x^34+216x^36+90x^38+29x^40+6x^42+5x^44+2x^46+1x^48+1x^56

The gray image is a linear code over GF(2) with n=136, k=10 and d=56.
This code was found by Heurico 1.16 in 0.0517 seconds.