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

generates a code of length 43 over Z2[X]/(X^3) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+34x^40+24x^42+128x^43+48x^44+8x^46+12x^48+1x^80

The gray image is a linear code over GF(2) with n=172, k=8 and d=80.
This code was found by Heurico 1.16 in 0.0286 seconds.