The generator matrix

 1  0  0  0  0  0  0  1  1  1  1  1  1  1  0  X  X  X  1  0  0  1  1  1  0  0  1  1  1  1  X  X  0  0  0  1  X  1  0  1
 0  1  0  0  0  0  0  0  0  0  0  0  0  X  1  1  1  1  1  1  1  X  1  1  X  1  0  1  X  0  1  X  X  0  1  1  1  1  1  0
 0  0  1  0  0  0  0  0  0  1  1  X X+1  1  1  1  0  1 X+1  0 X+1  X X+1  0  X  0  1 X+1 X+1 X+1  X  1  0  0  1  1 X+1 X+1  0  0
 0  0  0  1  0  0  0  0  1  0  X X+1  1 X+1  1  1 X+1 X+1 X+1  1  0  1  0 X+1  X  0 X+1  X X+1  X  0 X+1  1  1 X+1  0  0  X  1  0
 0  0  0  0  1  0  0  0  1  1  0 X+1  0  1 X+1  1  X  0  X  1  0  X  X  X  1  0 X+1  0  0  1 X+1 X+1 X+1  1 X+1 X+1  1  X  0  0
 0  0  0  0  0  1  0  1  0 X+1  X  X X+1  1 X+1  X X+1 X+1  0  0  X  X  X  X X+1 X+1  0 X+1  0  0  X  1 X+1  1  1  0  X  0 X+1  0
 0  0  0  0  0  0  1  1 X+1  X X+1  X  X X+1  X  1  0  1  X  1  0 X+1  1  0  0  X  1  0  1  X X+1  X X+1  0  1  1 X+1  1  0  0
 0  0  0  0  0  0  0  X  X  0  X  0  0  X  0  X  0  X  0  X  X  0  0  X  X  X  0  X  X  X  0  X  X  X  0  X  0  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+104x^28+114x^29+364x^30+490x^31+788x^32+900x^33+1304x^34+1422x^35+1773x^36+2316x^37+2493x^38+2830x^39+2636x^40+2992x^41+2522x^42+2452x^43+1974x^44+1490x^45+1294x^46+878x^47+677x^48+348x^49+292x^50+110x^51+101x^52+32x^53+49x^54+10x^55+10x^56+2x^58

The gray image is a linear code over GF(2) with n=80, k=15 and d=28.
This code was found by Heurico 1.11 in 25.8 seconds.