The generator matrix

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

generates a code of length 71 over Z7[X]/(X^2) who´s minimum homogenous weight is 410.

Homogenous weight enumerator: w(x)=1x^0+3150x^410+42x^411+714x^412+1356x^413+2730x^414+1596x^415+2898x^416+11844x^417+462x^418+3822x^419+2682x^420+5208x^421+2352x^422+4074x^423+13524x^424+714x^425+4620x^426+2838x^427+5208x^428+2268x^429+2562x^430+13020x^431+840x^432+5250x^433+3666x^434+5376x^435+2016x^436+2814x^437+9912x^438+30x^441+42x^448+6x^455+12x^462

The gray image is a linear code over GF(7) with n=497, k=6 and d=410.
This code was found by Heurico 1.16 in 76.6 seconds.