The SLIC has an audio output.  Let's hook that up to the mic input of the laptop.  As wikipedia shows, there are different pinouts standards  for a TRRS 3.5mm audio jack.  In other words, there's no standard pinout.  Use a DMM to find out what pinout your laptop is using.  My Acer has the following pinout:

• Tip = Left out
• Ring1 = Right out
• Ring2 = GND
• Sleeve = Mic in

In Ubuntu Linux, 5s of audio can easily be recorded by:

arecord -d 5 DTMF_0123456789.wav

To play back the file:

aplay DTMF_0123456789.wav

The microphone level might need some tuning.

Decode the DTMF-audio with:

multimon -a DTMF -t wav DTMF_0123456789.wav 
multimod  (C) 1996/1997 by Tom Sailer HB9JNX/AE4WA
available demodulators: POCSAG512 POCSAG1200 POCSAG2400 EAS AFSK1200 AFSK2400 AFSK2400_2 HAPN4800 FSK9600 DTMF ZVEI CCIR SCOPE
Enabled demodulators: DTMF
sox WARN sox: Option `-s' is deprecated, use `-e signed-integer' instead.
sox WARN sox: Option `-2' is deprecated, use `-b 16' instead.
DTMF: 0
DTMF: 1
DTMF: 2
DTMF: 3
DTMF: 4
DTMF: 5
DTMF: 6
DTMF: 7
DTMF: 8
DTMF: 9

Decoding works perfectly.

Alternative DTMF decoders

• MT8870 DTMF Audio Decoder LCD 1602 Display Module for Fixed telephone mobile phone keypad Key value shows smart home
• wholesale 1pcs MT8870 DTMF Voice decoding module phone module
• You could also download a DTMF decoder for your smartphone from Google Play.