ICC Calibration (Profile) for more bright black on LED screen

I have an IPS LED screen and I don’t like its black because it is very dark. I know it’s a bit strange (is it?) but I want the black to be more bright (that means grey) without white becoming darker. A dark blue would naturally become more bright then too and so on.

The contrast setting in the LED screen is already adjusted very low, so I think an ICC Profile would be good to make it better. It shall be an ICC Profile which is active the whole time in Windows which is strictly speaking called calibration file (ICM).

I can describe my desired transformation with 4 numbers and a principle but won’t insist on it exactly:

• 0 (black) to grey (0.3)
• 1 (white) to 1 (white)
• linear interpolation in between

so I think there should be a simple icc file or software to create it for my purpose? I have already digged in some icc files and saw some complicated color spaces which would be overwhelming to dig into for my purpose.