The generator matrix

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

generates a code of length 34 over Z2[X]/(X^3) who´s minimum homogenous weight is 29.

Homogenous weight enumerator: w(x)=1x^0+36x^29+76x^30+104x^31+130x^32+140x^33+142x^34+112x^35+88x^36+68x^37+40x^38+32x^39+17x^40+12x^41+14x^42+8x^43+3x^44+1x^52

The gray image is a linear code over GF(2) with n=136, k=10 and d=58.
This code was found by Heurico 1.16 in 0.0487 seconds.