Characteristic impedance depends on various factors as shown in the picture below.
Looks like for the stack up that you are using for the trace to be realistically wide enough the Z0 will have to be around 500 Ohm. As you can see I tried to replicate your stackup and to achieve Z0 as low as 390Ohm the trace would have to be around 100 mils which is highly unrealistic.
If your design is high speed, ie if impedance mismatch is going to cause issues in the proper working of your design then, I would suggest you use an industry standards as 0.062"4 layer stack up or your particular manufacturer's guidelines or mark one of the electrical layers as a plane layer (still a bit unrealistic but definitely less than 390 Ohm.)
- Kanchan Vaidya
Place a plane to referring Z0
Vaidya show Stackup editor from Hyperlynx, this is more smart then Xped/Pads