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

generates a code of length 40 over Z2[X]/(X^2) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+36x^38+7x^40+2x^42+7x^44+8x^46+2x^50+1x^52

The gray image is a linear code over GF(2) with n=80, k=6 and d=38.
This code was found by Heurico 1.16 in 21.9 seconds.