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
 0  X  0  0  0  0  0  X  0  0  0  X  X  0  X  X  0  0  X  0  0  X  X  0  0  X  X  X  X  0  0  0  0  X  X  X  0  0  0  X
 0  0  X  0  0  0  0  X  0  0  X  X  0  X  X  0  0  X  X  0  0  0  0  X  X  X  0  X  0  0  0  X  X  X  X  0  0  0  X  X
 0  0  0  X  0  0  0  X  0  X  X  0  0  X  0  X  0  0  X  0  X  X  0  X  0  0  X  X  0  0  X  X  0  0  X  X  X  X  X  0
 0  0  0  0  X  0  0  X  0  X  0  0  X  X  X  0  X  0  X  X  0  0  X  0  X  0  X  X  0  X  X  0  0  0  0  X  X  X  X  X
 0  0  0  0  0  X  0  X  X  0  0  0  X  X  0  X  X  0  0  X  X  0  0  0  0  X  X  X  X  0  0  X  X  0  0  X  X  X  0  X
 0  0  0  0  0  0  X  X  X  0  X  0  0  0  X  X  0  X  0  X  0  0  X  0  X  X  X  0  0  X  X  0  0  X  X  0  X  0  X  0

generates a code of length 40 over Z2[X]/(X^2) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+14x^34+24x^36+18x^38+142x^40+18x^42+24x^44+14x^46+1x^80

The gray image is a linear code over GF(2) with n=80, k=8 and d=34.
This code was found by Heurico 1.16 in 0.016 seconds.