Tuning Gmapping Parameters or Alternative SLAM Algorithm

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We built our own robotic platform with a home made LIDAR which is composed of four Time of Flight Sensors to get range information of the environment. For odometry information we are using optical encoders. I recorded a rosbag file to save /scan /odom /tf topics which are obtained in real life setup. Unfortunately, I couldn't be able to get nice mapping performance. I tried several parameters and I digged into gmapping parameters.

Here is my best case gmapping parameters:

<param name="base_frame" value="$(arg set_base_frame)"/>
<param name="odom_frame" value="$(arg set_odom_frame)"/>
<param name="map_frame"  value="$(arg set_map_frame)"/>
<param name="map_update_interval" value="2.0"/>
<param name="maxUrange" value="3.0"/>
<param name="sigma" value="0.05"/>
<param name="kernelSize" value="1"/>
<param name="lstep" value="0.05"/>
<param name="astep" value="0.05"/>
<param name="iterations" value="5"/>
<param name="lsigma" value="0.075"/>
<param name="ogain" value="3.0"/>
<param name="lskip" value="0"/>
<param name="minimumScore" value="10"/>
<param name="srr" value="0.01"/>
<param name="srt" value="0.02"/>
<param name="str" value="0.01"/>
<param name="stt" value="0.02"/>
<param name="linearUpdate" value="0.05"/>
<param name="angularUpdate" value="0.2"/>
<param name="temporalUpdate" value="0.5"/>
<param name="resampleThreshold" value="0.5"/>
<param name="particles" value="100"/>
<param name="xmin" value="-10.0"/>
<param name="ymin" value="-10.0"/>
<param name="xmax" value="10.0"/>
<param name="ymax" value="10.0"/>
<param name="delta" value="0.01"/>
<param name="llsamplerange" value="0.01"/>
<param name="llsamplestep" value="0.01"/>
<param name="lasamplerange" value="0.005"/>
<param name="lasamplestep" value="0.005"/>

My home made LIDAR properties:

360 Degree
64 point
1 Hz

I know that my LIDAR is not perfect, but I moved very slowly while recording rosbags. How can I improve the mapping performance? Do you know any other SLAM algorithm which could provide better performance for my case?

Here is a link to download my recorded bag file: real_data5.bag

EDIT1: Here is the gmapping result for these parameters.

EDIT2: oko_cartographer.launch file to call necessary cartographer_ros nodes with given kamu_robotu.lua (this lua file is provided below by @allenh1 : oko_cartographer.launch:

 <launch>
  <param name="/use_sim_time" value="true" />

  <node name="cartographer_node" pkg="cartographer_ros"
      type="cartographer_node" args="
          -configuration_directory $(find cartographer_ros)/configuration_files
          -configuration_basename kamu_robotu.lua"
      output="screen">
  </node>

  <node name="cartographer_occupancy_grid_node" pkg="cartographer_ros"
      type="cartographer_occupancy_grid_node" args="-resolution 0.05" />
</launch>

EDIT3: Here is my cartographer_ros result.

I really appreciate for your help. Thanks in advance!