This is a tricky one. It seems that there are some bigger spikes in the ACF. You may want to try MA with order 4, 10, 17 and 19 then check the residuals after fitting the model.
Please try Ljung-Box test with different lags (8, 12, 16 etc). I guess some of the results should support no autocorrelations. Your test with 20 lags may be one of the occasions that give you an exceptional result.