The generator matrix

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

generates a code of length 62 over Z7[X]/(X^2) who´s minimum homogenous weight is 355.

Homogenous weight enumerator: w(x)=1x^0+966x^355+126x^356+378x^357+672x^358+1932x^359+2772x^360+3486x^361+6132x^362+1134x^363+2910x^364+4074x^365+5586x^366+4452x^367+5334x^368+8232x^369+1764x^370+4038x^371+4242x^372+6552x^373+3948x^374+5334x^375+6552x^376+3150x^377+5268x^378+5418x^379+6510x^380+5292x^381+4368x^382+6930x^383+42x^385+36x^392+18x^399

The gray image is a linear code over GF(7) with n=434, k=6 and d=355.
This code was found by Heurico 1.16 in 4.57 seconds.