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

generates a code of length 64 over Z7[X]/(X^2) who´s minimum homogenous weight is 361.

Homogenous weight enumerator: w(x)=1x^0+252x^361+828x^364+378x^365+42x^366+168x^367+2604x^368+5190x^371+1806x^372+756x^373+1260x^374+4116x^375+8472x^378+2898x^379+4536x^380+5208x^381+8316x^382+17832x^385+5796x^386+9072x^387+7770x^388+8736x^389+12738x^392+3528x^393+4788x^396+138x^399+150x^406+102x^413+60x^420+60x^427+42x^434+6x^441

The gray image is a linear code over GF(7) with n=448, k=6 and d=361.
This code was found by Heurico 1.16 in 44.7 seconds.