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

generates a code of length 40 over Z2[X]/(X^2) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+97x^32+16x^34+179x^36+112x^38+242x^40+112x^42+150x^44+16x^46+71x^48+23x^52+4x^56+1x^64

The gray image is a linear code over GF(2) with n=80, k=10 and d=32.
This code was found by Heurico 1.16 in 0.143 seconds.