The generator matrix

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

generates a code of length 38 over Z2[X]/(X^3) who´s minimum homogenous weight is 37.

Homogenous weight enumerator: w(x)=1x^0+12x^37+38x^38+7x^40+4x^41+1x^46+1x^54

The gray image is a linear code over GF(2) with n=152, k=6 and d=74.
This code was found by Heurico 1.16 in 0.0199 seconds.