I contacted ESRI regarding this issue and they said the grid is not available via ArcObjects. However, they did demonstrate how to add a coded value domain to the list view:
'Create the list table
Dim valueTableParameter As IGPParameterEdit = New GPParameterClass()
valueTableParameter.DataType = New GPValueTableTypeClass()
valueTableParameter.Value = New GPValueTableClass()
valueTableParameter.Direction = esriGPParameterDirection.esriGPParameterDirectionInput
valueTableParameter.DisplayName = "Input params table"
valueTableParameter.Name = "Grid"
valueTableParameter.ParameterType = esriGPParameterType.esriGPParameterTypeRequired
Dim stringColumn As IGPStringType = New GPStringTypeClass()
Dim inputLayerType As DEFileType = New DEFileTypeClass()
Dim valueTableType As IGPValueTableType = New GPValueTableTypeClass()
valueTableType.AddDataType(CType(inputLayerType, IGPDataType), "Input Features", 70, Nothing)
valueTableType.AddDataType(TryCast(stringColumn, IGPDataType), "Attribute", 100, Nothing)
valueTableParameter.DataType = TryCast(valueTableType, IGPDataType)
Dim valueTable As IGPValueTable = New GPValueTableClass()
valueTable.AddDataType(CType(inputLayerType, IGPDataType))
valueTable.AddDataType(TryCast(stringColumn, IGPDataType))
Dim attributeCodedValueDomain As IGPCodedValueDomain = New GPCodedValueDomainClass()
Const sCodes As String = "Code 1, Code 2, Code 3"
attributeCodedValueDomain.PopulateDomain(sCodes, sCodes, DirectCast(stringColumn, IGPDataType))
' Create a composite domain and add two domains, one for each column
Dim gpValueTableTypeDomain As IGPCompositeDomain = New GPCompositeDomainClass()
gpValueTableTypeDomain.AddDomain(Nothing) 'Don't want a domain on the file type. Could use IGPFileDomain if we did
gpValueTableTypeDomain.AddDomain(DirectCast(attributeCodedValueDomain, IGPDomain))
'Bind the Composite domain to the ValueTable ParameterEdit
valueTableParameter.Domain = DirectCast(gpValueTableTypeDomain, IGPDomain)
valueTableParameter.Value = TryCast(valueTable, IGPValue)
pParameters.Add(valueTableParameter)