The generator matrix

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

generates a code of length 83 over Z7[X]/(X^2) who´s minimum homogenous weight is 482.

Homogenous weight enumerator: w(x)=1x^0+2940x^482+3432x^483+1680x^484+504x^485+1218x^486+1932x^487+1092x^488+8988x^489+9216x^490+2814x^491+1848x^492+2352x^493+3192x^494+1092x^495+8736x^496+9480x^497+3360x^498+1848x^499+2226x^500+2520x^501+1008x^502+10836x^503+9126x^504+2814x^505+1974x^506+2436x^507+2646x^508+924x^509+7602x^510+6078x^511+1680x^512+24x^518+18x^525+6x^532+6x^539

The gray image is a linear code over GF(7) with n=581, k=6 and d=482.
This code was found by Heurico 1.16 in 6.09 seconds.