The generator matrix

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

generates a code of length 24 over Z7[X]/(X^2) who´s minimum homogenous weight is 126.

Homogenous weight enumerator: w(x)=1x^0+246x^126+534x^133+2058x^138+438x^140+12348x^145+384x^147+438x^154+282x^161+78x^168

The gray image is a linear code over GF(7) with n=168, k=5 and d=126.
This code was found by Heurico 1.16 in 0.0914 seconds.