The generator matrix

 1  0  0  0  0  1  1  1  0  X  1  1  1  1  1  X  1  1  1  X  X  0  0  1  X  1  X  0  1  1  1  0  1  1  X  1  1  X  X  1
 0  1  0  0  0  X  X  X  X  1  1  1  X  0  1  1 X+1 X+1  X  X  X  1  X  1  1 X+1  1  X X+1  0 X+1  1  X X+1  0  X  X  1  X  0
 0  0  1  0  0  0  0  X  0  0  X  X X+1  1 X+1 X+1  1  0  1  1  X X+1  1  1  1  X  X  1  X X+1 X+1  1 X+1  0  0 X+1  1  0  1  0
 0  0  0  1  0  0 X+1 X+1  1  X  0  X  X X+1  1  0  X  1  1 X+1  1  0  X  X  1  1 X+1 X+1  0 X+1 X+1 X+1 X+1  1  1  1  0  1  X  0
 0  0  0  0  1  1 X+1  X X+1 X+1  1  0  1  1 X+1  1  0  X  0  0 X+1  X  1 X+1  1 X+1  X X+1  1  1  0  1 X+1 X+1 X+1  X  0  1 X+1  X

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+98x^34+223x^36+168x^38+131x^40+144x^42+95x^44+88x^46+56x^48+14x^50+6x^52

The gray image is a linear code over GF(2) with n=80, k=10 and d=34.
This code was found by Heurico 1.16 in 0.105 seconds.