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

generates a code of length 56 over Z7[X]/(X^2) who´s minimum homogenous weight is 315.

Homogenous weight enumerator: w(x)=1x^0+240x^315+570x^322+294x^324+462x^329+3528x^331+300x^336+10584x^338+270x^343+120x^350+138x^357+162x^364+48x^371+72x^378+18x^385

The gray image is a linear code over GF(7) with n=392, k=5 and d=315.
This code was found by Heurico 1.16 in 0.27 seconds.