Well, this is a little longer than one line!
If you don't want to think too hard, you can find the expected value experimentally -- Just do a million (or so) status rolls see what the average is. Note the array-slice of the sort, which finds the 3 highest dice with much less mucky-muck.
use List::Util 'sum';
my ($iter, $sum) = shift || 1_000_000;
$sum += sum +(sort map {1 + int rand 6} 1..4)[1..3] for 1..$iter;
print $sum/$iter, $/;
For a million iterations, I got an expected value of 12.244657, which is within 0.0005% of your exact answer.
You could also use some of the Die/Dice modules on CPAN, but rolling (fair) dice is pretty trivial to do yourself.
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