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

generates a code of length 42 over Z2[X]/(X^3) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+35x^38+28x^39+20x^40+104x^41+147x^42+96x^43+20x^44+24x^45+25x^46+4x^47+7x^48+1x^82

The gray image is a linear code over GF(2) with n=168, k=9 and d=76.
This code was found by Heurico 1.16 in 0.0442 seconds.