The generator matrix

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

generates a code of length 81 over Z7[X]/(X^2) who´s minimum homogenous weight is 470.

Homogenous weight enumerator: w(x)=1x^0+3528x^470+3150x^471+252x^472+504x^473+1218x^474+1512x^475+3276x^476+11004x^477+6720x^478+966x^479+966x^480+2310x^481+2604x^482+3504x^483+12978x^484+8694x^485+1428x^486+1260x^487+2310x^488+2016x^489+3144x^490+11592x^491+7182x^492+1470x^493+1386x^494+2394x^495+2100x^496+2712x^497+10290x^498+5124x^499+24x^504+12x^511+12x^518+6x^525

The gray image is a linear code over GF(7) with n=567, k=6 and d=470.
This code was found by Heurico 1.16 in 5.77 seconds.