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

generates a code of length 80 over Z7[X]/(X^2) who´s minimum homogenous weight is 441.

Homogenous weight enumerator: w(x)=1x^0+366x^441+1230x^448+1638x^455+1956x^462+7206x^469+33498x^476+65244x^483+1662x^490+1572x^497+1278x^504+960x^511+576x^518+318x^525+108x^532+30x^539+6x^553

The gray image is a linear code over GF(7) with n=560, k=6 and d=441.
This code was found by Heurico 1.16 in 18.8 seconds.