The generator matrix

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

generates a code of length 82 over Z7[X]/(X^2) who´s minimum homogenous weight is 483.

Homogenous weight enumerator: w(x)=1x^0+2622x^483+798x^484+2646x^485+2802x^490+546x^491+882x^492+1230x^497+336x^498+2646x^499+1890x^504+378x^505+6x^511+6x^518+18x^525

The gray image is a linear code over GF(7) with n=574, k=5 and d=483.
This code was found by Heurico 1.16 in 0.649 seconds.