This Pro tutorial shows how we can prefilter the results of a query output by a Bricks query loop to only those for which the value of a specified custom field is not blank.
Edit your query loop and toggle the Query editor (PHP) on.
Paste
return [
'meta_query' => [
[
'key' => 'short_quote',
'compare' => 'EXISTS',
],
[
'key' => 'short_quote',
'value' => '',
'compare' => '!=',
],
],
];
Repalce both instances of short_quote with the name/ID of your custom field.

This will output posts for which the specified custom field exists and is not empty.
It could be a bug in the current version of Bricks, but the same does not work using the META QUERY GUI option in the Bricks query popup.