Thunno, \$ 18 \log_{256}(96) \approx \$ 14.82 bytes

34C"34C+sc9/"+sc9/

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Based off @Mukundan314's Pyth answer.

Explanation

34C                 # Push chr(34), the double quote
   "34C+sc9/"+      # Prepend it to the string "34C+sc9/"
              sc    # Swap and count the number of times the input is in the string
                9/  # Divide by 9 (Half the length of the program)

Thunno, \$ 18 \log_{256}(96) \approx \$ 14.82 bytes

34C"34C+sc9/"+sc9/

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Based off @Mukundan314's Pyth answer.

Thunno, \$ 6 \log_{256}(96) \approx \$ 4.94 bytes

zdsc6/

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Probably cheating but I'll put it here anyway.

Explanations

34C                 # Push chr(34), the double quote
   "34C+sc9/"+      # Prepend it to the string "34C+sc9/"
              sc    # Swap and count the number of times the input is in the string
                9/  # Divide by 9 (Half the length of the program)

zd      # Push the source code
  sc    # Swap and count the number of times the input is in the string
    6/  # Divide by 6 (The length of the program)

Thunno, \$ 36 \log_{256}(96) \approx \$ 29.63 bytes

"D34CXx+xs+s+sc36/"D34CXx+xs+s+sc36/

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Based off @PkmnQ's 05AB1E answer. Uses @lyxal's Thunno quine.

Explanation

"D34CXx+xs+s+sc36/"D34CXx+xs+s+       # Quine bits
                               sc     # Swap and count the number of times the input is in the string
                                 36/  # Divide by 36 (The length of the program)

Thunno, \$ 18 \log_{256}(96) \approx \$ 14.82 bytes

34C"34C+sc9/"+sc9/

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Based off @Mukundan314's Pyth answer.

Explanation

34C                 # Push chr(34), the double quote
   "34C+sc9/"+      # Prepend it to the string "34C+sc9/"
              sc    # Swap and count the number of times the input is in the string
                9/  # Divide by 9 (Half the length of the program)