My half-assed try... 67
for('00'..'99'){$a.=$_ unless $x{$_} or $x{reverse $_}++};print $a;
#234567890#234567890#234567890#234567890#234567890#234567890#234567
# 1 2 3 4 5 6
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Note, it includes '00' which some people are missing...
Update... 59? (similar to hardburn's solution)
for('00'..'99'){$x{$_}++unless $x{reverse()}};print keys%x;
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Update 2 ...50?
for$a(0..9){for(0..9){$x.="$a$_"if$_>=$a}}print$x;
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Update 3: after a clarification, i guess i've misunderstood the problem. I thought it needed all unique pairs, separately (ie. 00, 01, 02, 03...). My bad.
Update 4: Here's one that actually passes the checker (60)
$_=9;for$a(0..9){for$b($a..9){$_.="$a$b"}s/$a{3}/$a$a/}print
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Update... 57!
$_=9;for$a(0..9){for$b($a..9){$_.="$a$b"}s/$a$a/$a/}print
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--
"To err is human, but to really foul things up you need a computer." --Paul Ehrlich