I doubt you will get there with a single IC. Gain bandwidth product is just what it says. Gain times bandwidth. So with a gain of 1 you need a bandwidth of 3.6 Mhz. Multiply that times 47 and there is a problem. Slew rate is not quite so bad. It is volts per usec. of output swing or about 11.
Might be better to expain the objective to see if there is another way to get there.
actually, to properly calculate the bandwidth and slew rate, one thing that must be known is the required rise/ fall times of the pulse, and not just the period (or is the 140nS the "on" time?)
Do you need to accurately reproduce the pulse shape and height or do you just want to just generate a higher voltage pulse (which a high speed comparator could do)?