No. There is not a code to pay your late tax due. TurboTax will not calculate late penalties or interest for you. The IRS/state will do that and they will send you a bill after they receive the payment for the tax due as shown on your tax return.
If you have federal tax due you can pay by mailing your payment with the 1040V voucher, (which has the address printed on it, having the payment taken out of a designated bank account, or you can pay directly on the IRS website.
https://ttlc.intuit.com/community/tax-payments/help/how-can-i-pay-my-federal-taxes/00/26212
To apply for a payment plan with the IRS
Apply Online for a Payment Plan
You must pay your state tax due using the state’s preferred method of receiving payment. For most states that will be by making a payment to the state’s own tax website, or by mailing a check or money order.
https://ttlc.intuit.com/questions/1901670-how-do-i-contact-my-state-department-of-revenue
the IRS and probably the state would calculate penalties based on the postmark on the envelope you use to mail payment. the IRS has Direct Pay so you can pay today and most state's website offer a method of electronic payment.