Yes, you can deduct eligible reimbursed moving expenses that are shown in box 1 of your W-2. These will be claimed on Form 3903, Moving Expenses. Code “P” in box 12 wouldn’t be relevant, anyway, since that would represent fringe benefits that aren't deductible.
Since your employer reimbursed the expenses, they’re almost surely “qualified” expenses, but you might look at the TurboTax article IRS Moving Expense Deductions to verify.
To enter your job-related moving expenses in TurboTax,
1. Open (continue) your return, if it isn’t already open.
2. Inside TurboTax, search for “3903”, then click the "Jump to" link.
3. Answer Yes to “Did you have any work-related moving expenses?”
4. Follow the onscreen instructions.