I can see some answers have been supplied to solve the problem of entering the values into an Hash via a mapped grep. I have looked at the initial problem of identifying multiple values within each line. The aligned families can be retrieved using an array reading loop. However I caqn imagine further data manipulation would mean having the families in a hash may be more helpful in future reference. Here is how I would initially extract the multiple values via an array loop.

use strict;
use warnings;

my $gendata = './gen.dat';
open GENDAT, "< $gendata" or die "can't open $gendata $!";
my @count;

while (<GENDAT>){
 push @count, $_;
}
close GENDAT;

my $a=shift @count;
my @families=split(/\s+/,$a);
my $b=0;

foreach my $c(@count){
  my @state;
  push @state, split(/\s+/,$c);
  print $state[0].' ';
    
    for($b=0;$b<=$#state;$b++){
     print $families[$b].' ' if $state[$b] eq '1';
    }
  print $/;
}


exit (0);
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this gives:

OG_1 lacM mori
OG_2 taba glyB
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A different approach might be assigning values to each of the families and then extract the 01 strings and convert them into a binary then return the relevant family pair as determined by the binary value. Of course this would only work if there were a definite 2 unique families per 'OG'.