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

generates a code of length 28 over Z7[X]/(X^2) who´s minimum homogenous weight is 161.

Homogenous weight enumerator: w(x)=1x^0+138x^161+2178x^168+54x^175+6x^182+24x^196

The gray image is a linear code over GF(7) with n=196, k=4 and d=161.
This code was found by Heurico 1.16 in 0.00445 seconds.