A slight variation on toolic's approach:

perl -wMstrict -le
"my $data = qq{Log foo bar baz \n}
          . qq{aaa 123 456 789 \n}
          . qq{bbb 987 654 321 \n}
          ;
 ;;
 open my $fh, '<', \$data or die qq{opening data: $!};
 ;;
 my (undef, @dim2_names) = split /\s+/, <$fh>;
 print qq{      @dim2_names};
 ;;
 my %hash_2d;
 while (defined(my $rec = <$fh>)) {
   my ($row, @vals) = split /\s+/, $rec;
   print qq{$row = @vals};
   @{ $hash_2d{$row} }{ @dim2_names } = @vals;
   }
 ;;
 use Data::Dumper;
 print Dumper \%hash_2d;
"
      foo bar baz
aaa = 123 456 789
bbb = 987 654 321
$VAR1 = {
          'bbb' => {
                     'bar' => '654',
                     'baz' => '321',
                     'foo' => '987'
                   },
          'aaa' => {
                     'bar' => '456',
                     'baz' => '789',
                     'foo' => '123'
                   }
        };
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