The generator matrix

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

generates a code of length 34 over Z2[X]/(X^3) who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+220x^31+117x^32+208x^33+64x^34+188x^35+48x^36+48x^37+100x^39+24x^40+4x^43+2x^48

The gray image is a linear code over GF(2) with n=136, k=10 and d=62.
This code was found by Heurico 1.16 in 54.1 seconds.