Don't know if this is more Perlish, but this also seems to give the same results, also produces 'null' zeroth elements:

use strict;
use warnings;

my $string =
    "BEHACJBDLCENADFEGOFHQAGIHJRBIKJLSCKMLNTDMOFNPOQTGPRIQSKRTMPS";

my @result = (
  [ 0, 0, 0, 0, ],
  # map [ 0, map $_ -= 64, unpack 'C*', $_ ],  # -= is pointless
  map [ 0, map $_ - 64, unpack 'C*', $_ ],
  unpack '(a3)*', $string
  );


# Print the results

for my $i (1..20) {
    for my $j (1..3) {
        print sprintf("%02d", $result[$i][$j]) . " ";
    }
    print "\n";
}
[download]

Output:

02 05 08
01 03 10
02 04 12
03 05 14
01 04 06
05 07 15
06 08 17
01 07 09
08 10 18
02 09 11
10 12 19
03 11 13
12 14 20
04 13 15
06 14 16
15 17 20
07 16 18
09 17 19
11 18 20
13 16 19
[download]

Update: $_ -= 64 in map statement is pointless waste of computrons. Changed to $_ - 64 per oshalla's reply below.