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

generates a code of length 22 over Z7[X]/(X^2) who´s minimum homogenous weight is 112.

Homogenous weight enumerator: w(x)=1x^0+96x^112+534x^119+384x^126+14406x^132+528x^133+420x^140+318x^147+120x^154

The gray image is a linear code over GF(7) with n=154, k=5 and d=112.
This code was found by Heurico 1.16 in 0.0829 seconds.