You guys are awesome....

@Merri:
Output of Merri's code in my PC:
Code:
72 64 53 27 86 31 81 33 68 85 45 42
77 39 54 27 12 55 24 35 53 73 89 5
68 28 60 27 29 52 36 46 47 26 20 14
54 63 60 27 11 53 12 47 56 4 25 49
84 85 60 27 32 82 54 47 8 50 41 39
41 18 62 27 63 6 88 49 79 73 25 83
2 41 62 27 35 75 40 50 68 9 28 74
60 5 63 27 22 31 54 51 65 68 35 90
77 51 63 27 26 76 52 53 33 78 14 79
11 75 63 27 37 83 5 53 46 44 60 69
6 3 64 27 58 82 39 53 1 12 7 44
72 15 64 27 65 3 66 53 6 16 69 89
83 29 64 27 56 71 90 53 59 80 40 50
64 49 65 27 58 26 38 54 45 71 44 31
36 61 64 27 7 40 60 54 62 28 41 73
49 70 64 27 26 69 77 54 22 19 25 16
Did you noticed that the 4th row is showing the same result (27) !

@EdgeMeal:
It took 124 seconds without any modification and 134 seconds when I used DoEvents like this:
Code:
'...
'.....
'......
' if no match then add to UniqArray
    If i > UBound(UniqArray) Then
        UniqArray(n) = sTmp
        DoEvents
        List1.AddItem sTmp
        n = n + 1 ' increment position for UniqArray
'......
'....
'..
...

I'll test my code now...
Ah! The test result is: 241 seconds for 31999 sequences
Tested code:
Code:
Option Explicit

Private Sub Command1_Click()
    
    Dim OutputArray(11)     As Byte     '~~~ This will hold the numbers generated using the function
    Dim strUni(31999)           As String
    Dim strOutput           As String   '~~~ Final result
    Dim strTemp             As String
    Dim n                   As Long
    Dim i                   As Long
    Dim t                   As Single
    
    t = Timer
    Do While n < 31999
        If n > 0 Then
            strTemp = StrConv(OutputArray, vbUnicode)   '~~~ Getting the unicode string for the generated array values
            i = 0
            Do While i < 31999                              '~~~ We are going to check this unicode value with others.
                If strTemp = strUni(i) Then             '~~~ If it is matched, then the array is shuffled and the checking is restarted.
                    ShuffleArray OutputArray            '~~~ Shuffle the array
                    strTemp = StrConv(OutputArray, vbUnicode)   '~~~ Unicode value of the shuffled array
                    i = 0                               '~~~ Start the checking (loop) from the beginning
                Else
                    i = i + 1
                End If
            Loop
        End If
        
        strUni(n) = mySequence(OutputArray) '~~~ Storing the unicode string of the present byte array values
        
        '~~~ Creating that line of sequence of the present byte array values
        For i = 0 To 11
            strOutput = strOutput & " " & OutputArray(i)
        Next
        
        
        List1.AddItem strOutput
        strOutput = ""
        n = n + 1
    Loop
    
    MsgBox Timer - t & " - " & List1.ListCount
End Sub

Private Function mySequence(ByRef myOrder() As Byte) As String
    Randomize
    
    Dim myArray(1 To 90)    As Boolean
    Dim num                 As Byte
    Dim counter             As Integer
    
    Do While counter < 12           '~~~ 12 values (for each line)
        num = Int(Rnd * 90 + 1)     '~~~ Finding a random number from 1 to 90
        If myArray(num) = False Then    '~~~ Check if it is already selected
            myArray(num) = True         '~~~ Marking it as selected number
            myOrder(counter) = num      '~~~ Storing the number
            counter = counter + 1
        End If
    Loop
    mySequence = StrConv(myOrder, vbUnicode)    '~~~ Returning the unicode value of this byte array

End Function

' Knuth shuffle (very fast). Thanks to "Ellis Dee" for this shuffle code
Public Function ShuffleArray(pvarArray As Variant)
    Dim i As Long
    Dim iMin As Long
    Dim iMax As Long
    Dim lngReplace As Long
    Dim varSwap As Variant
    
    iMin = LBound(pvarArray)
    iMax = UBound(pvarArray)
    For i = iMax To iMin + 1 Step -1
        lngReplace = Int((i - iMin + 1) * Rnd + iMin)
        varSwap = pvarArray(i)
        pvarArray(i) = pvarArray(lngReplace)
        pvarArray(lngReplace) = varSwap
    Next
End Function
I think its time for upgrading my PC...