The generator matrix

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

generates a code of length 58 over Z7[X]/(X^2) who´s minimum homogenous weight is 336.

Homogenous weight enumerator: w(x)=1x^0+372x^336+294x^337+840x^339+588x^340+1764x^341+1998x^343+882x^344+1260x^346+588x^347+588x^348+636x^350+294x^351+2016x^353+882x^354+1764x^355+1404x^357+588x^358+30x^364+18x^371

The gray image is a linear code over GF(7) with n=406, k=5 and d=336.
This code was found by Heurico 1.16 in 0.123 seconds.