The generator matrix

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

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+2646x^121+7056x^122+462x^126+13230x^128+18816x^129+14406x^132+1890x^133+27342x^135+31752x^136+6x^147+42x^154

The gray image is a linear code over GF(7) with n=154, k=6 and d=121.
This code was found by Heurico 1.16 in 1.12 seconds.