I just modified my 54 bits/line solution to do base 50 math like you suggested to get 51 bits/line.

It does work --- but ---it is SLOW!!!

#!/usr/bin/perl

# https://perlmonks.org/?node_id=1233613

use strict;
use warnings;
use bignum;

my @legal = grep !/11/ && tr/1// <= 3, glob '{0,1}' x 8;
my %code;
@code{@legal} = 0 .. $#legal;
my %decode = reverse %code;
$_ = [ split ' ', '23456789' & tr/01/ ?/r ] for values %decode;

sub tobits
  {
  my $n = shift;
  my $bits = '';
  $bits = $n % 2 . $bits, $n >>= 1 for 1 .. 51;
  $bits;
  }

sub tonum
  {
  my $n = 0;
  $n = 2 * $n + $_ for split //, shift;
  $n;
  }

#print tobits(42), "\n";
#exit;

sub compress
  {
  my $coded = '';
  for ( shift =~ /(.*)\n/g )
    {
    my @lookup = (0) x 123;
    @lookup[ unpack 'C*', $_ ] = (1) x length;
    my $n = 0;
    for( my $group = 35; $group < 123; $group += 10 )
      {
      $n = $n * 50 + $code{ join '', @lookup[$group .. $group + 7] };
      }
#   print "$n\n";
    $coded .= tobits($n);
    }
  return pack 'b*', $coded;
  }

sub decompress
  {
  my $decoded = '';
  for my $line ( unpack('b*', shift) =~ /.{51}/g )
    {
    my $n = tonum($line);
#   print "$n\n";
    my $digit = 8;
    for( my $group = 33; $group < 123; $group += 10 )
      {
      $decoded .= pack 'C*',
        map $group + $_, @{ $decode{ int $n / 50 ** $digit % 50 } };
      $digit--;
      }
    $decoded .= "\n";
    }
  return $decoded;
  }

my $input = '';
for (1 .. 80)
  {
  for (my $x=0; $x<90; $x+=10)
    {
    my @c;
    push(@c, int (rand(10)+$x));
    push(@c, int (rand(10)+$x));
    push(@c, int (rand(10)+$x));
    push(@c, int (rand(10)+$x));
    @c = sort{$a<=>$b}@c;
    for (my $i = 1; $i < @c; $i++)
      {
      $input .= chr(33+$c[$i]) if $c[$i] != $c[$i-1] && $c[$i] != $c[$
+i-1]+1;
      }
    }
  $input .= "\n";
  }

#use Data::Dump 'dd'; dd $_ for $input =~ /.*\n/g;
print "\n     input length ", length $input, "\n";

my $compressed = compress($input);
my $compressedlength = length $compressed;
print "compressed length $compressedlength\n";
my $restored = decompress($compressed);
if( $input eq $restored )
  {
  printf "\nMatched, compression ratio = %.1f%%\n",
    100 * (1 - length($compressed) / length($restored));
  }
else
  {
  print "----------------------------------------failed\n";
  use Data::Dump 'dd'; dd $_ for $restored =~ /.*\n/g;
  }
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