Tell me please is there any way to boot catalyst 3750 (3560, 2960) switch from tftp?
*.bin file is 20MB
Ok then. I think I know WHY you are in this predicament. Anyways ...
Download the IOS version 12.2(55)SE. For a 3750 with only 16mb of flash, this version (55) is the highest you can go. It says so in the 12.2(58)SE Release Notes.