Here is a fairly simple solution that nobody seems to have suggested. It processes the data line by line, pulling all the integers from each line into an array using a simple regex with the g quantifier, then reverse sorts the array, and finally prints the first element. The code is probably a bit more verbose than it needs to be, but that is deliberate as you mention that you are new to PERL Perl.

#!/usr/bin/perl -w
use strict;

# Read each line one by one
while (my $line = <DATA>) {
    chomp($line);   # Dispense with trailing newline
    # Extract everything that looks like an integer into an array
    my @ints = $line =~ m/(\d+)/g;
    # Sort the array, highest to lowest
    my @sorted_ints = reverse sort { $a <=> $b } @ints;

    # Ouput the line, and the highest integer (1st element of the sort
+ed array)
    print "DATA:$line\nHIGHEST INTEGER:$sorted_ints[0]\n";
}

__DATA__
ASBSDEC 34 GADVVEEVEETTE 56 IOEOREAK GKJEOG EFEAF 1090 DAFFEE 376
ASB C 134 PPKOREAK EFEAF 290
BLAH 99 BLAH 123 FRED 27 BARNEY 427
[download]

Output:

DATA:ASBSDEC 34 GADVVEEVEETTE 56 IOEOREAK GKJEOG EFEAF 1090 DAFFEE 376
HIGHEST INTEGER:1090
DATA:ASB C 134 PPKOREAK EFEAF 290
HIGHEST INTEGER:290
DATA:BLAH 99 BLAH 123 FRED 27 BARNEY 427
HIGHEST INTEGER:427
[download]

Hope this helps,
Darren :)