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

generates a code of length 28 over Z7[X]/(X^2) who´s minimum homogenous weight is 147.

Homogenous weight enumerator: w(x)=1x^0+144x^147+444x^154+438x^161+14856x^168+354x^175+318x^182+216x^189+36x^196

The gray image is a linear code over GF(7) with n=196, k=5 and d=147.
This code was found by Heurico 1.16 in 0.115 seconds.