If you set $/ to a reference to the number of (virtual) grid columns, then open a filehandle to a reference to your string, you can then read each (virtual) grid row as a separate record and perform your matching on each distinct row-record.

$ perl -Mstrict -Mwarnings -Mautodie -le '
    sub match_virtual_grid_rows {
        local $/ = \shift;
        open my $fh, "<", \shift;
        grep { /(.)\1\1/ } <$fh>;
    }

    my $virtual_grid_columns = 5;
    my $grid_string = "ABCBBBCBADBCCACDDDAC";
    print for match_virtual_grid_rows($virtual_grid_columns, $grid_str
+ing);
'
DDDAC
[download]

A couple of additional tests: