The information on the Form 1099-R regarding the meaning of the codes does not provide the usage details for the codes. Yes, code 4 means a distribution made to a beneficiary, but code 4 is not to be used for any distribution from a Roth IRA, it's only to be used for distributions to beneficiaries of all other types of accounts subject to reporting on Form 1099-R.
The instructions for Form 1099-R provide the code-usage requirements:
https://www.irs.gov/pub/irs-pdf/i1099r.pdf
If it's truly a Roth IRA and your mother had the account for more than 5 years, Form 8606 does not apply because the distribution is a qualified distribution. Only nonqualified Roth IRA distributions are to be reported on Form 8606 Part III. Also, the IRS knows that distributions reported with code 4 are not to appear on Form 8606 Part III because code 4 indicates that the distribution is not a distribution from a Roth IRA.
You need to get this sorted out with the payer and, if it's truly a Roth IRA, obtain a corrected code 4 Form 1099-R showing that $0 was distributed as a code-4 distribution and obtain a new Form 1099-R showing the distribution with code Q. (This method provides a clearer indication to the IRS than the payer just issuing a single Form 1099-R showing correction of the code, which the IRS would have to correlate by the reported account number.)
