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

generates a code of length 24 over Z7[X]/(X^2) who´s minimum homogenous weight is 133.

Homogenous weight enumerator: w(x)=1x^0+60x^133+138x^140+2058x^144+84x^147+18x^154+12x^161+30x^168

The gray image is a linear code over GF(7) with n=168, k=4 and d=133.
This code was found by Heurico 1.16 in 0.00354 seconds.