The generator matrix

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

generates a code of length 83 over Z7[X]/(X^2) who´s minimum homogenous weight is 476.

Homogenous weight enumerator: w(x)=1x^0+750x^476+504x^477+126x^478+714x^480+1092x^481+3510x^483+4284x^484+1638x^485+1764x^487+1932x^488+5940x^490+7182x^491+2562x^492+3654x^494+3822x^495+7476x^497+15624x^498+5922x^499+5124x^501+4830x^502+8724x^504+13986x^505+4158x^506+3150x^508+2730x^509+4326x^511+1638x^512+132x^518+114x^525+108x^532+42x^539+42x^546+24x^553+6x^560+18x^567

The gray image is a linear code over GF(7) with n=581, k=6 and d=476.
This code was found by Heurico 1.16 in 10 seconds.