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

generates a code of length 22 over Z7[X]/(X^2) who´s minimum homogenous weight is 126.

Homogenous weight enumerator: w(x)=1x^0+180x^126+2058x^132+96x^133+18x^140+12x^147+36x^154

The gray image is a linear code over GF(7) with n=154, k=4 and d=126.
This code was found by Heurico 1.16 in 0.00366 seconds.