Use grep to extract only the elements you require.

#!/usr/bin/env perl 
use strict;
use warnings;
use Data::Dumper;

my @array = (
    ['X1','X2','X3','X4' ],
    ['','foo','',''],
    ['bar','','','']
);

my @nofirstempty = grep { length $_->[0] } @array;
print Dumper \@nofirstempty;
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