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Gnuplot gives unusually large error ratings

Today I tried to fit the experimental data using this theoretical model. Although the match was pretty good, gnuplot returned extremely high errors:

Final set of parameters            Asymptotic Standard Error
=======================            ==========================

A               = 1.76654e-11      +/- 2.589e-06    (1.465e+07%)
g               = 0.000929911      +/- 1.006e-05    (1.082%)
offset          = 0.831727         +/- 0.005273     (0.634%)
x0              = 25.7152          +/- 3768         (1.465e+04%)

In particular, the error for x0 is an important measure for my next calculations. Obviously, this value is absolutely absurd, as can be seen in the figure below.

What do I need to do to get a meaningful error?

screenshot

MWE:

f(x,x0,g) = -16.0*A*(g*(g**2.0-12.0*(x-x0)**2))/(pi*(g**2.0+4.0*(x-x0)**2.0)**3.0) + offset
FIT_LIMIT = 1e-16

A=-1e-3
g=1e-3
offset=0.8
x0 = 25.71514200

fit f(x,x0,g) "data" via A,g,offset,x0

plot "data", f(x,x0,g)

Data: Link (pastebin)

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, 3- . , x0 g . fit (- via...) (- f(x,x0,g)).

""? , .

:

f(x) = -16.0*A*(g*(g**2.0-12.0*(x-x0)**2))/(pi*(g**2.0+4.0*(x-x0)**2.0)**3.0) + offset
FIT_LIMIT = 1e-16

A=-1e-3
g=1e-3
offset=0.8
x0 = 25.71514200

fit f(x) "data" via A,g,offset,x0

plot "data", f(x)
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