The generator matrix

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

generates a code of length 80 over Z7[X]/(X^2) who´s minimum homogenous weight is 464.

Homogenous weight enumerator: w(x)=1x^0+1470x^464+5712x^465+252x^466+588x^467+2184x^468+1566x^469+1512x^470+6762x^471+9618x^472+1764x^473+2646x^474+3234x^475+2850x^476+1890x^477+7896x^478+12432x^479+1890x^480+2352x^481+2856x^482+1950x^483+1386x^484+7434x^485+11340x^486+2268x^487+2646x^488+4074x^489+2124x^490+1386x^491+5250x^492+8232x^493+36x^497+24x^504+18x^511+6x^525

The gray image is a linear code over GF(7) with n=560, k=6 and d=464.
This code was found by Heurico 1.16 in 6.34 seconds.