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

generates a code of length 26 over Z7[X]/(X^2) who´s minimum homogenous weight is 140.

Homogenous weight enumerator: w(x)=1x^0+432x^140+504x^147+438x^154+14406x^156+378x^161+318x^168+258x^175+72x^182

The gray image is a linear code over GF(7) with n=182, k=5 and d=140.
This code was found by Heurico 1.16 in 93.9 seconds.