The generator matrix

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

generates a code of length 63 over Z7[X]/(X^2) who´s minimum homogenous weight is 361.

Homogenous weight enumerator: w(x)=1x^0+1260x^361+42x^362+378x^363+756x^364+2100x^365+2772x^366+3948x^367+6090x^368+714x^369+2142x^370+2958x^371+7602x^372+4200x^373+5922x^374+7014x^375+1386x^376+3402x^377+4584x^378+6720x^379+4452x^380+5712x^381+7938x^382+1974x^383+4368x^384+4314x^385+8274x^386+5040x^387+4998x^388+6510x^389+36x^392+30x^399+12x^406

The gray image is a linear code over GF(7) with n=441, k=6 and d=361.
This code was found by Heurico 1.16 in 4.69 seconds.