The generator matrix

 1  0  1  1  1  1  1  1  1  1  1  0  1  1  1  1  1  1  1  1  X  1
 0  1  1  3 5X+2  6 5X+4  5  0 5X+1  3  1 5X+2  5  X 5X+1 X+3  6 X+6 X+5 4X 4X+4
 0  0 5X 3X 6X  X 2X 3X  X 4X 2X  X 5X  0 4X 2X  X 6X 5X 6X 3X 3X

generates a code of length 22 over Z7[X]/(X^2) who´s minimum homogenous weight is 121.

Homogenous weight enumerator: w(x)=1x^0+378x^121+1260x^122+180x^126+1890x^128+3360x^129+96x^133+3906x^135+5670x^136+18x^140+12x^147+36x^154

The gray image is a linear code over GF(7) with n=154, k=5 and d=121.
This code was found by Heurico 1.16 in 0.0842 seconds.