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

generates a code of length 58 over Z7[X]/(X^2) who´s minimum homogenous weight is 322.

Homogenous weight enumerator: w(x)=1x^0+84x^322+168x^323+42x^327+336x^328+678x^329+756x^330+168x^331+1554x^333+1218x^334+2982x^335+2550x^336+2016x^337+1260x^338+4158x^340+2268x^341+5502x^342+2862x^343+2730x^344+5208x^345+11718x^347+6048x^348+11634x^349+6420x^350+5208x^351+7770x^352+11382x^354+4830x^355+8358x^356+3672x^357+3528x^358+210x^364+96x^371+102x^378+48x^385+48x^392+24x^399+12x^406

The gray image is a linear code over GF(7) with n=406, k=6 and d=322.
This code was found by Heurico 1.16 in 4.91 seconds.