The generator matrix

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

generates a code of length 39 over Z2[X]/(X^3) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+54x^34+64x^35+105x^36+128x^37+121x^38+128x^39+93x^40+128x^41+67x^42+64x^43+51x^44+11x^46+4x^48+1x^50+2x^56+2x^58

The gray image is a linear code over GF(2) with n=156, k=10 and d=68.
This code was found by Heurico 1.16 in 0.0475 seconds.