Thermal vibration will make the atoms move about 10^−11 m. Therefore you won't be able to measure the length of line with a precision better than that. Therefore you will be able to encode without loss only 9 decimal digits, or 7.8 hexadecimal digits.
Also, you have to consider where you print this line. Paper expands depending on ambiant humidity, with factors on the order of 0.05%, which means that you will be able to encode without loss only 3 or 5 decimal digits.
If you print it on something like a metalic piece, then expansion will depend on the temperature, between 4.5 for W and 61 for He, so you won't be able to encode any digit.
Unless you calibrate and maintain a controlled environment, such for example, the very costly and sophisticated controlled environment maintained around the etalon meter (before the meter was redefined in function of the speed of light and the duration of 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom).