The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1
 0  X  0  0  0  X  X 4X  0 3X  X 6X 2X 6X  0 5X 6X 4X  X  X 5X  X 6X
 0  0  X  0  0 5X 4X 5X  X 4X 5X 5X  X  X  X 3X  X 6X 6X 4X 5X 5X  0
 0  0  0  X  0 5X 3X 3X 5X 5X  X 6X  0 2X 6X 2X  X  0  X 5X  0 3X  X
 0  0  0  0  X 5X 6X  X 6X  X  X  0 2X  X  X 4X 6X 3X 4X 2X  X 6X 2X

generates a code of length 23 over Z7[X]/(X^2) who´s minimum homogenous weight is 112.

Homogenous weight enumerator: w(x)=1x^0+684x^112+1278x^119+1980x^126+14406x^132+2934x^133+86436x^139+3972x^140+3672x^147+1848x^154+438x^161

The gray image is a linear code over GF(7) with n=161, k=6 and d=112.
This code was found by Heurico 1.16 in 7.9 seconds.