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

generates a code of length 56 over Z7[X]/(X^2) who´s minimum homogenous weight is 301.

Homogenous weight enumerator: w(x)=1x^0+486x^301+1158x^308+1644x^315+2004x^322+2034x^329+14406x^330+2250x^336+86436x^337+1962x^343+1992x^350+1716x^357+954x^364+486x^371+96x^378+24x^385

The gray image is a linear code over GF(7) with n=392, k=6 and d=301.
This code was found by Heurico 1.16 in 12.1 seconds.