The generator matrix

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

generates a code of length 82 over Z7[X]/(X^2) who´s minimum homogenous weight is 469.

Homogenous weight enumerator: w(x)=1x^0+210x^469+42x^474+552x^476+756x^481+456x^483+4536x^488+342x^490+9072x^495+210x^497+162x^504+108x^511+96x^518+84x^525+60x^532+72x^539+18x^546+24x^553+6x^560

The gray image is a linear code over GF(7) with n=574, k=5 and d=469.
This code was found by Heurico 1.16 in 0.475 seconds.