The generator matrix

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

generates a code of length 24 over Z7[X]/(X^2) who´s minimum homogenous weight is 112.

Homogenous weight enumerator: w(x)=1x^0+198x^112+822x^119+1368x^126+2106x^133+14406x^138+2886x^140+86436x^145+3798x^147+3354x^154+1878x^161+396x^168

The gray image is a linear code over GF(7) with n=168, k=6 and d=112.
This code was found by Heurico 1.16 in 4.04 seconds.