The generator matrix

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

generates a code of length 40 over Z2[X]/(X^2) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+213x^28+502x^30+1452x^32+2128x^34+4024x^36+5006x^38+6011x^40+5056x^42+4122x^44+2274x^46+1335x^48+368x^50+216x^52+26x^54+33x^56+1x^60

The gray image is a linear code over GF(2) with n=80, k=15 and d=28.
This code was found by Heurico 1.16 in 60 seconds.