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  X  X  X  X  1  X  X  X  X  1
 0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  0  0  X  X  X  0  X  X  X  0  0  X  X  X  0  0  0  X  0
 0  0  X  0  0  0  0  0  0  0  0  0  X  0  0  X  X  X  X  X  X  0  0  0  0  0  X  X  X  0  0  X  X  0  0  0  X  X  X  X
 0  0  0  X  0  0  0  0  0  0  0  0  X  X  X  X  X  0  X  X  X  0  X  X  X  0  X  0  0  X  0  0  X  X  0  X  0  X  X  0
 0  0  0  0  X  0  0  0  0  0  0  X  0  X  X  0  X  X  X  0  X  X  X  0  0  0  0  0  X  0  X  X  0  0  X  X  0  0  0  X
 0  0  0  0  0  X  0  0  0  0  0  X  0  0  X  X  X  X  X  0  0  X  0  0  X  X  0  0  0  X  0  0  X  0  X  X  X  0  X  X
 0  0  0  0  0  0  X  0  0  0  X  0  0  0  X  X  0  0  X  0  0  X  X  0  X  0  X  0  X  X  X  0  X  X  0  0  X  0  0  X
 0  0  0  0  0  0  0  X  0  0  X  0  0  X  0  0  X  0  0  X  0  X  X  0  0  X  X  X  0  X  0  X  X  0  X  0  X  X  0  0
 0  0  0  0  0  0  0  0  X  0  X  X  X  X  0  0  0  0  X  0  0  0  X  X  X  X  0  0  0  X  0  X  X  0  X  X  0  0  0  0
 0  0  0  0  0  0  0  0  0  X  X  X  X  0  0  X  X  X  X  X  0  X  0  X  0  X  0  X  X  X  X  X  0  0  X  0  X  0  0  X

generates a code of length 40 over Z2[X]/(X^2) who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+57x^30+122x^32+131x^34+184x^36+329x^38+408x^40+331x^42+208x^44+115x^46+76x^48+49x^50+24x^52+11x^54+1x^58+1x^64

The gray image is a linear code over GF(2) with n=80, k=11 and d=30.
This code was found by Heurico 1.16 in 4.58 seconds.