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

generates a code of length 57 over Z7[X]/(X^2) who´s minimum homogenous weight is 322.

Homogenous weight enumerator: w(x)=1x^0+360x^322+516x^329+432x^336+14406x^342+306x^343+204x^350+192x^357+132x^364+132x^371+42x^378+66x^385+12x^392+6x^399

The gray image is a linear code over GF(7) with n=399, k=5 and d=322.
This code was found by Heurico 1.16 in 0.276 seconds.