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

generates a code of length 29 over Z7[X]/(X^2) who´s minimum homogenous weight is 154.

Homogenous weight enumerator: w(x)=1x^0+174x^154+534x^161+396x^168+14406x^174+432x^175+306x^182+354x^189+162x^196+42x^203

The gray image is a linear code over GF(7) with n=203, k=5 and d=154.
This code was found by Heurico 1.16 in 0.121 seconds.