这是一个使用Kotlin和Volley库发送Multipart请求并获取JSONObject响应的示例代码。我们需要创建一个名为VolleyFileUploadRequest的类，它将扩展Volley的Request类并实现Multipart请求。我们还需要使用Volley的JsonRequest类来获取服务器的响应。

以下是示例代码：

class VolleyFileUploadRequest(
    method: Int,
    url: String,
    private val files: Map,
    private val headers: MutableMap?,
    private val listener: Response.Listener,
    errorListener: Response.ErrorListener
) : Request(method, url, errorListener) {

    private val boundary = "volleymultipart3266"
    private val volleyQueue: RequestQueue = Volley.newRequestQueue(App.getContext())

    override fun getHeaders(): MutableMap {
        val headers = headers ?: HashMap()
        headers["Content-Type"] = "multipart/form-data;boundary=$boundary"
        return headers
    }

    @Throws(AuthFailureError::class)
    override fun getBody(): ByteArray {
        val outputStream = ByteArrayOutputStream()
        val dataOutputStream = DataOutputStream(outputStream)

        try {
            for ((key, value) in files) {
                dataOutputStream.writeBytes("--$boundary\r\n")
                dataOutputStream.writeBytes("Content-Disposition: form-data; name=\"$key\"; filename=\"${value.name}\"" + "\r\n")
                dataOutputStream.writeBytes("\r\n")
                dataOutputStream.write(value.readBytes())
                dataOutputStream.writeBytes("\r\n")
            }
            dataOutputStream.writeBytes("--$boundary--\r\n")
            dataOutputStream.flush()
        } catch (e: IOException) {
            e.printStackTrace()
        }
        return outputStream.toByteArray()
    }

    override fun parseNetworkResponse(response: NetworkResponse?): Response {
        var jsonString = String(response?.data ?: ByteArray(0), Charset.forName(HttpHeaderParser.parseCharset(response?.headers)))
        return try {
            Response.success(JSONObject(jsonString), HttpHeaderParser.parseCacheHeaders(response))
        } catch (e: Exception) {
            Response.error(ParseError(e))
        }
    }

    override fun deliverResponse(response: JSONObject?) {
        listener.onResponse(response)
    }

    override fun deliverError(error: VolleyError?) {
        super.deliverError(error)
    }

    fun execute() {
        volleyQueue.add(this)
    }
}

为了使用VolleyFileUploadRequest，我们需要将所需的参数传递给构造函数，并在需要时调用execute（）函数。我们可以像这样使用它：

val url = "https://example.com/upload"