The generator matrix

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

generates a code of length 38 over Z2[X]/(X^3) who�s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+60x^34+162x^35+118x^36+216x^37+83x^38+116x^39+55x^40+88x^41+26x^42+42x^43+21x^44+16x^45+15x^46+4x^48+1x^52

The gray image is a linear code over GF(2) with n=152, k=10 and d=68.
This code was found by Heurico 1.16 in 0.0385 seconds.