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

generates a code of length 29 over Z7[X]/(X^2) who´s minimum homogenous weight is 168.

Homogenous weight enumerator: w(x)=1x^0+162x^168+2058x^174+120x^175+30x^182+6x^189+24x^203

The gray image is a linear code over GF(7) with n=203, k=4 and d=168.
This code was found by Heurico 1.16 in 0.0052 seconds.