How do I convert image into QR code in C# ?

ZXing is a great option indeed as @Mehedi Gholam suggested.
This could be in the list too: Open Source QRCode Library[^]

A few other great alternative are described here:
Free c# QR-Code generator - Stack Overflow[^]

fails due to storage size ?
Probably yes. I think you should change your question to "what is the max length of a string that a QR code supports".

You can refer to wikipedia[^].

Numeric only	7,089	3⅓	0, 1, 2, 3, 4, 5, 6, 7, 8, 9
Alphanumeric	4,296	5½	0–9, A–Z (upper-case only), space, $, %, *, +, -, ., /, :
Binary/byte	2,953	8	ISO 8859-1
Kanji/kana	1,817	13	Shift JIS X 0208

A base64 string is used for encoding an image. If the image size is big, the length of the string may be greater than the limitation supported by QR code. Therefore, my suggestion is that don't convert a base64 string to QR code! No matter which SDK you use, ZXing, Dynamsoft Barcode Reader and so on, you may fail to encode the string.