The generator matrix

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

generates a code of length 82 over Z7[X]/(X^2) who´s minimum homogenous weight is 476.

Homogenous weight enumerator: w(x)=1x^0+3084x^476+3990x^477+1302x^478+504x^479+630x^480+2352x^481+2604x^482+7662x^483+7938x^484+2352x^485+1806x^486+1008x^487+3570x^488+2940x^489+10314x^490+9366x^491+2562x^492+1932x^493+1386x^494+3444x^495+2478x^496+8178x^497+10290x^498+3192x^499+1932x^500+1092x^501+2982x^502+2268x^503+8100x^504+5460x^505+882x^506+12x^511+18x^518+12x^525+6x^532

The gray image is a linear code over GF(7) with n=574, k=6 and d=476.
This code was found by Heurico 1.16 in 6.02 seconds.