The generator matrix

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

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+138x^455+474x^462+444x^469+372x^476+14406x^480+276x^483+222x^490+102x^497+102x^504+84x^511+72x^518+24x^525+54x^532+18x^539+6x^546+6x^553+6x^560

The gray image is a linear code over GF(7) with n=560, k=5 and d=455.
This code was found by Heurico 1.16 in 0.458 seconds.