Transpose and Groupby pandas Columns

I’m looking to transpose pandas columns and apply a Groupby

df = pd.DataFrame({'ID' : ['ID1', 'ID2', 'ID3', 'ID4'], 
                   'Code1' : ['X60', np.nan, 'X66', np.nan], 
                   'Code2' : [np.nan, 'X64', 'X78', np.nan],
                   'Code3' : [np.nan, 'X66', 'X81', 'X59'],
                   'Code4' : [np.nan, np.nan, 'X38', 'X60']})
df

    ID      Code1   Code2   Code3   Code4
0   ID1     X60     NaN     NaN     NaN
1   ID2     NaN     X64     X66     NaN
2   ID3     X66     X78     X81     X38
3   ID4     NaN     NaN     X59     X60

How can I achieve this expected output ?

Code NB ID
X38  1  ID3
X59  1  ID4
X60  2  ID1, ID4 
X64  1  ID2
X66  2  ID2, ID3
X78  1  ID3
X81  1  ID3

Answer

Use DataFrame.stack for reshape with remove missing values and count values by Series.value_counts, last Series.sort_index with Series.rename_axis and Series.reset_index for 2 columns DataFrame:

df = df.stack().value_counts().sort_index().rename_axis('Code').reset_index(name='NB')
print (df)
  Code  NB
0  X38   1
1  X59   1
2  X60   2
3  X64   1
4  X66   2
5  X78   1
6  X81   1

EDIT: Use DataFrame.melt and then aggregate by size and join in GroupBy.agg:

df = (df.melt('ID', value_name='Code')
        .groupby('Code', as_index=False)
        .agg(NB=('Code','size'), ID=('ID',', '.join)))
print (df)
  Code  NB        ID
0  X38   1       ID3
1  X59   1       ID4
2  X60   2  ID1, ID4
3  X64   1       ID2
4  X66   2  ID3, ID2
5  X78   1       ID3
6  X81   1       ID3