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

generates a code of length 63 over Z7[X]/(X^2) who´s minimum homogenous weight is 357.

Homogenous weight enumerator: w(x)=1x^0+606x^357+168x^358+504x^359+1050x^361+6156x^364+1512x^365+1470x^366+2142x^368+12642x^371+2688x^372+3150x^373+3444x^375+29844x^378+5880x^379+5796x^380+5124x^382+24576x^385+4158x^386+3486x^387+2646x^389+186x^392+126x^399+132x^406+72x^413+48x^420+24x^427+6x^434+12x^441

The gray image is a linear code over GF(7) with n=441, k=6 and d=357.
This code was found by Heurico 1.16 in 5.32 seconds.