Constructing a 12VDC to 230VAC 1-phase inverter
I suspect that you are under-driving the low-voltage primary. 

That 12-0-12 rating on the low-voltage side is the RMS value of the AC. The peak voltage, when used as a regular mains transformer, will be \$ 12\sqrt 2 \$. Since you are driving it with a peak of 12 V then the output could be expected to be \$ \frac {230}{\sqrt 2} = 162 \ \text V \$ which is very close to your reading.

You need to increase the turns ratio by \$ \sqrt 2 \$. An 8.5 - 0 - 8.5 transformer would be ideal.