The generator matrix

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

generates a code of length 34 over Z2[X]/(X^3) who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+50x^30+102x^31+283x^32+118x^33+58x^34+72x^35+162x^36+64x^37+34x^38+18x^39+41x^40+10x^41+10x^42+1x^48

The gray image is a linear code over GF(2) with n=136, k=10 and d=60.
This code was found by Heurico 1.11 in 0.016 seconds.