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

generates a code of length 84 over Z7[X]/(X^2) who´s minimum homogenous weight is 482.

Homogenous weight enumerator: w(x)=1x^0+462x^482+438x^483+168x^484+2016x^486+5124x^489+1728x^490+1512x^491+5922x^493+7854x^496+2712x^497+2688x^498+9828x^500+9870x^503+6342x^504+5880x^505+16254x^507+14154x^510+4974x^511+4158x^512+9198x^514+5754x^517+162x^518+96x^525+126x^532+78x^539+42x^546+66x^553+18x^560+24x^567

The gray image is a linear code over GF(7) with n=588, k=6 and d=482.
This code was found by Heurico 1.16 in 30.9 seconds.