Pyth, 252¹¹¹ ≈ 3.593 × 10²⁶⁶

Js[
"ixL-rC1`H``N"
N
s@L-rC1`H``NjQ252
N
"252")$import sys$$sys.stdout.buffer.write(J.encode('iso-8859-1'))$

Had to use a little bit of Python syntax, because Pyth's print can't print in iso-8859-1.

The number gets encoded in base 252 and represent each digit in that base as an iso-8859-1 char. The chars \ and " would need escaping, and therefore are not used. The char ` isn't used because golfing... And additionally the null-byte is also not used, the Pyth compiler forbids it.

The output is a program with an overhead of 17 bytes:

ixL-rC1`H``N""252

Here's an example usage with the biggest number possible:

Explanation

of the output program.

ixL-rC1`H``N""252
    rC1`H          create the range of chars: ['\x01', '\x02', ..., '{}']
         ``N       creates a string containing the 3 chars " ' \
   -               remove strings which consists of these 3 chars
 xL         ""     determine the index of each char in "" (encoded number)
i             252  convert from base 253 to base 10