No, code B is for designated Roth (401k Roth) accounts.
Code J is necessary since you have to pay taxes on the earnings from the excess contribution. Only the earnings are in box 2a (taxable amount).
The IRS states:
"You must include in your gross income the interest or other income that was earned on the excess contribution. Report it on your return for the year in which the excess contribution was made."
@Taxn00b15
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