Can I define my ranking position out of the below information?

Yes, you can compute the z score for each of the boundard conditions below, fit a straight line through the data, find the z-score for your score on that line then find the probability that corresponds to. This assumes normality. If the line isn't very straight, then this isn't a good assumption. One challange is defining the boundary conditions. Is 104 the 90th percentile or is it 93? (I'd use 93.5) I tried it for fun. Here are the z-scores:

103.5 1.281551566
95.5 0.385320466
89.5 -0.439913166
85.5 -1.22652812

That makes a decent line and your percentile would be 87.6%

I meant 103 and 103.5.

Thanks for your help!