It can be cleaned up a little using statement modifiers and defaults for split:

use strict;
use warnings;

my $word="test";
while(<DATA>) {
     next if ! /\b($word)\b/;
     
     my @arr = split;
     my $col = "";
     my $i=0;
     foreach my $k (@arr) {
         $i++;
         $col .= "$i\t" if $k eq $word;
     }
    
     print "The word repeated in Line $. and in column $col\n";
}

__DATA__
This is a test from tester okay
nothing
message test center test
test in proress ... test one test two
[download]

Prints:

The word repeated in Line 1 and in column 4    
The word repeated in Line 3 and in column 2    4    
The word repeated in Line 4 and in column 1    5    7
[download]