Direct evaporation custom coil design.

Hi everybody,
after a deep search in the posts, I did not find anything that fits to my problem so I will post the question directly.
I must refrigerate a reservoir containing 2 litres of ethanol (0.52 gallons) at -40°C (-40°F) and I need (roughly taking into account the thermal leaks) 100W of refrigerating power @-40°C.
I am willing to use R404A as refrigerant with a direct expansion in a copper tube coil immersed into the reservoir.

I must compute the length of the coil in order to transfer all the heat I need and make sure to sufficiently superheat the vapour to eliminate the risk of liquid in the compressor.

I tried to use the TechniSolve DXC package but, as far as I understand, only finned coils for air refrigeration are taken into account.

Thank you all in advance.

(Just to give an idea, I attach the cycle I am trying to implement)

Well, even a rule of thumb would be useful.