What diode i should use for inductive spike suppression when i will drive 40 A 48V DC motor?
Any speciffic diode woud be nice. I do not know how to find correct one.

One that can handle 40A pulses (continuous rating can be less, say 20A), and perhaps 100V or
more reverse voltage rating. There are many suitable devices, a parametric search ordered
by price is one way to choose a suitable one. You might have requirements for the type of package,
such as screw-terminal or whatever.

ok , so the parameter that i should look at for amps is Continuous Forward Current or different one ?

Ideally 'continuos' as your load may have sufficient mechanical inertia to drive the motor as a generator whose output should go somewhere.

...when i will drive 40 A 48V DC motor?

Drive on/off, or PWM speed control.
Fast recovery diode is needed for PWM.
When driven with a mosfet H-bridge (forward/reverse), no diodes are needed.

The part how it works and so on i get but i have difficulty to choose spacific diode for my motor, i will be using MBR20L80CT but this is just guesing from my little knowledge so it is not reliable thats why i am asking for help