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

generates a code of length 69 over Z7[X]/(X^2) who´s minimum homogenous weight is 397.

Homogenous weight enumerator: w(x)=1x^0+1470x^397+1344x^398+396x^399+336x^400+1134x^401+420x^402+4242x^403+8904x^404+5502x^405+1752x^406+1512x^407+2688x^408+420x^409+6762x^410+10290x^411+8106x^412+2838x^413+2142x^414+2982x^415+546x^416+6090x^417+11508x^418+7770x^419+3492x^420+2184x^421+3486x^422+672x^423+5544x^424+8988x^425+4032x^426+30x^427+18x^434+24x^441+18x^448+6x^455

The gray image is a linear code over GF(7) with n=483, k=6 and d=397.
This code was found by Heurico 1.16 in 5.22 seconds.