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

generates a code of length 80 over Z7[X]/(X^2) who´s minimum homogenous weight is 455.

Homogenous weight enumerator: w(x)=1x^0+126x^455+252x^456+378x^461+4464x^462+1008x^463+1764x^468+12150x^469+2058x^470+3024x^475+20526x^476+3192x^477+5670x^482+32394x^483+4788x^484+3570x^489+18738x^490+3108x^491+126x^497+78x^504+48x^511+30x^518+48x^525+30x^532+60x^539+6x^546+12x^553

The gray image is a linear code over GF(7) with n=560, k=6 and d=455.
This code was found by Heurico 1.16 in 7.14 seconds.