Codegolf the sequence of distance-3 Hamming Codewords (A075926)
Python 2, 98 97 bytes

-1 byte thanks to Mr. Xcoder


x=input()
l=[]
i=0
while len(l)&lt;x:s=any(bin(i^n).count('1')&lt;3for n in l);i+=s;l+=[i]*-~-s
print l


Try it online!

Straightforward implementation, using xor to calculate the hamming distance.
The inner loop is equivalent to :

if any(bin(i^n).count('1')&lt;3 for n in l):
   i+=1
else:
   l.append(i)