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

generates a code of length 31 over Z7[X]/(X^2) who´s minimum homogenous weight is 168.

Homogenous weight enumerator: w(x)=1x^0+324x^168+516x^175+450x^182+14406x^186+342x^189+324x^196+252x^203+144x^210+48x^217

The gray image is a linear code over GF(7) with n=217, k=5 and d=168.
This code was found by Heurico 1.16 in 0.126 seconds.