The generator matrix

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

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+68x^28+130x^29+309x^30+446x^31+742x^32+852x^33+1168x^34+1588x^35+1905x^36+2280x^37+2520x^38+2788x^39+2821x^40+2928x^41+2685x^42+2448x^43+1947x^44+1594x^45+1239x^46+814x^47+605x^48+364x^49+242x^50+108x^51+95x^52+44x^53+26x^54+7x^56+1x^58+1x^60+2x^62

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 63.2 seconds.