The generator matrix

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

generates a code of length 81 over Z7[X]/(X^2) who´s minimum homogenous weight is 476.

Homogenous weight enumerator: w(x)=1x^0+3798x^476+6378x^483+2244x^490+4356x^497+6x^504+24x^511

The gray image is a linear code over GF(7) with n=567, k=5 and d=476.
This code was found by Heurico 1.16 in 0.214 seconds.