Read your if statement, you essentially say that if the last modified time of the directory is greater than 2 minutes ago, print "Not modified within last 2 minute". This is clearly not what you want to do. Here is a slightly tidied up version, see also File::stat which is a core module, and Basic debugging checklist.

#!/bin/usr/perl

use strict;
use warnings;

my $modified_within = 2 * 60;
my $InputDir = "/home/marto/derpderp";
my $LastModified = (stat($InputDir))[9];
my $CurrentTime = time;

if ( $LastModified > ($CurrentTime - $modified_within) ){
  print "Modified in last 2 minutes\n";
}else{
  print "Not Modified in last 2 minutes\n";
}
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