This is fairly simple:

1. call to_paletted() with the quantization options you want, in your case max_colors => 16
2. call write()

For example

my $pal = $source->to_paletted
  (
   max_colors => 16,
   translate => "errdiff",
  ) or die $source->errstr;
$pal->write(file => "foo.png")
  or die $pal->errstr;
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That said, unless your images start with a small number of colours (non-photographic, no blends, little anti-aliasing) the results are going to be fairly ugly. You should test with some representative source images.