The generator matrix

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

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+1320x^322+714x^323+756x^327+7596x^329+3612x^330+2142x^334+14622x^336+6048x^337+5796x^341+29112x^343+11256x^344+5712x^348+21240x^350+7182x^351+174x^357+120x^364+102x^371+54x^378+66x^385+24x^392

The gray image is a linear code over GF(7) with n=399, k=6 and d=322.
This code was found by Heurico 1.16 in 46.4 seconds.