There's even a much simpler algorithm:

my $N    = 6;
my @nums = (0 .. $N * $N - 1);

my $grid;

foreach my $x (0 .. $N - 1) {
    foreach my $y (0 .. $N - 1) {
        push @$grid => [@nums];
        push @nums  => splice @nums => 0, $N;
    }
    foreach my $y (0 .. $N - 1) {
        splice @nums => $y * $N, $N =>
               @nums [($y * $N + 1) .. (($y + 1) * $N - 1), $y * $N]
    }
}
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Abigail