The generator matrix

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

generates a code of length 68 over Z7[X]/(X^2) who´s minimum homogenous weight is 392.

Homogenous weight enumerator: w(x)=1x^0+2766x^392+882x^393+1050x^394+1596x^395+2184x^396+1722x^397+2100x^398+9642x^399+2226x^400+2478x^401+4326x^402+3906x^403+3486x^404+2268x^405+11958x^406+3486x^407+4242x^408+5376x^409+4158x^410+2562x^411+2100x^412+10836x^413+5754x^414+4578x^415+5166x^416+4158x^417+2520x^418+1764x^419+8280x^420+36x^427+36x^434+6x^441

The gray image is a linear code over GF(7) with n=476, k=6 and d=392.
This code was found by Heurico 1.16 in 12.1 seconds.