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

generates a code of length 81 over Z7[X]/(X^2) who´s minimum homogenous weight is 462.

Homogenous weight enumerator: w(x)=1x^0+174x^462+4662x^468+1506x^469+13818x^475+2448x^476+23184x^482+4254x^483+37590x^489+5016x^490+21588x^496+3000x^497+102x^504+108x^511+18x^518+36x^525+48x^532+36x^539+36x^546+18x^553+6x^560

The gray image is a linear code over GF(7) with n=567, k=6 and d=462.
This code was found by Heurico 1.16 in 7.22 seconds.