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

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+450x^469+42x^471+168x^472+378x^473+2058x^475+4422x^476+1218x^478+1512x^479+1764x^480+4536x^482+7890x^483+2268x^485+2688x^486+3024x^487+6384x^489+10488x^490+6048x^492+5880x^493+5670x^494+10668x^496+14946x^497+4830x^499+4158x^500+3570x^501+5166x^503+7014x^504+78x^511+96x^518+60x^525+54x^532+60x^539+24x^546+18x^553+6x^560+6x^567+6x^574

The gray image is a linear code over GF(7) with n=574, k=6 and d=469.
This code was found by Heurico 1.16 in 7.2 seconds.