The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0 X^2  0  0  0  0  0  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0  0  0  0 X^2
 0  0 X^2  0  0  0  0  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0  0  0  0  0  0 X^2 X^2
 0  0  0 X^2  0  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0  0  0  0 X^2  0 X^2 X^2 X^2  0  0  0  0  0 X^2 X^2  0
 0  0  0  0 X^2  0 X^2 X^2 X^2  0  0  0  0  0 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0  0  0 X^2 X^2  0  0
 0  0  0  0  0 X^2 X^2  0 X^2 X^2  0  0  0 X^2 X^2  0  0 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2 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+6x^34+15x^36+212x^38+15x^40+6x^42+1x^76

The gray image is a linear code over GF(2) with n=152, k=8 and d=68.
This code was found by Heurico 1.16 in 0.019 seconds.