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

generates a code of length 59 over Z7[X]/(X^2) who´s minimum homogenous weight is 343.

Homogenous weight enumerator: w(x)=1x^0+918x^343+252x^344+1806x^346+882x^347+2850x^350+672x^351+1680x^353+294x^354+894x^357+1134x^358+2688x^360+882x^361+1812x^364+18x^371+6x^378+12x^385+6x^392

The gray image is a linear code over GF(7) with n=413, k=5 and d=343.
This code was found by Heurico 1.16 in 0.122 seconds.