That's about what I came up with.
In order to convert from mmol/L to mg/L you just have to multiply your measurement in mmol/L by the molar mass of CO2.

C- 12.01g/mol
O- 16.00g/mol

So 12.01g + 2(16.00g) = 44.01g CO2/mol

Your measurement of 4.2mmol/L x 44.01g CO2/mol = 184.842mg/l = 184.842ppm, so something is wrong with the measurement unless I messed up with my math (which is possible, haha).

I will show the whole equation so you can see all the units cancel out and change to achieve this result below. Notice how the two conversions just multiply and then divide by 1000 so you just have to multiply by molar mass and that's it.

Full equation-

(44.01g / 1 mol CO2)(1mol CO2/1000 mmol CO2)(4.2 mmol CO2/1L H2O)(1000mg/1g)

= 184.842 mg/L H2O, it also equals
= 184.842 ppm CO2 since 1mg/L = 1ppm in water.

Are you sure the measurement wasn’t 0.42mmol/L instead of 4.2mmol/L? If it was, that would then give you 18.4 mg/L or 18.4 ppm which would sound about perfect based on your parameters, and the fact that the kH vs. CO2 table has a tendency to inflate CO2 concentrations.

Yes i'm sure, this were the results. Ph 6.5, pco2 5.08 Kpa, po2 23.18 Kpa, hco3(activ) 2.9 mmol/l, hco3 (standard) 2.4 mmol/l, Co2 4.1 mmol/l and Base excess -38 mmol/l. The only thing wath is wrong that they measured with a temp of 37 degrees Celcius, but the real temp of the sample must be something about 20 degrees Celcius.

They use the 37 degrees celcius because of the blood temp. of human beings.
Could the temp. influance the outcome of the measurement??