You will have to use an op-amp configuration to amplify your low input voltage. I'm not sure if you're familiar with non-inverting op-amps...but if you aren't, here are links that will help you:
http://www.wisc-online.com/objects/ViewObject.aspx?ID=SSE7906
http://www.engga.uwo.ca/people/asamani/courses/ece238a/Labs/Lab6.pdf
http://www.play-hookey.com/analog/non-inverting_amplifier.html
http://www.wisc-online.com/objects/ViewObject.aspx?ID=SSE3003
I did some calculations but they're based on knowledge of op-amps. I'll include them anyway.
Using knowledge of a non-inverting op-amp (please reference the image I've attached), we have:
Eqn 1.\[V _{out} = V_{in}[(R _{1} +R _{2})/R _{1}] = V_{in}[1 + (R _{2}/R _{1})]\]Input voltage, Vin = 14V & output voltage, Vout ~ 220 - 300V. I'll pick 266 as Vout because it's a multiple of 14 and will give us a rational number as gain (which is simpler to work with). R1 & R2 are resistors in the op-amp configuration.
Using Eqn 1, here is the math!\[266 = 14(1 + (R _{2}/R _{1}))\]\[266/14 = 1 + (R _{2}/R _{1})\]\[19 = 1 +(R _{2}/R _{1})\]\[19 = (R _{1}+R _{2})/R _{1}\]\[19R _{1} = R _{1}+R _{2}\]\[19R _{1} - R _{1} = R _{2}\]\[18R _{1} = R _{2}\]
Now, you have a ratio that tells you \[R _{2}\] has to be 18 times greater than\[R _{1}\]for you to have a gain of 19. Recall that gain is just Vout/Vin. I suggest you pick resistor values ranging from \[1k \Omega -100K \Omega\]Another thing, your op-amp will need a power supply (of \[\pm -- V\]For example, an LM741 op-amp would need a power supply of \[\pm15V\]