The generator matrix

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

generates a code of length 64 over Z7[X]/(X^2) who´s minimum homogenous weight is 367.

Homogenous weight enumerator: w(x)=1x^0+1596x^367+168x^368+252x^369+588x^370+1602x^371+3066x^372+4200x^373+6216x^374+1008x^375+1680x^376+2478x^377+4728x^378+7308x^379+6804x^380+7434x^381+1890x^382+2940x^383+3570x^384+5022x^385+5292x^386+6132x^387+8610x^388+3108x^389+3360x^390+3654x^391+5382x^392+6972x^393+5502x^394+7014x^395+30x^399+24x^406+18x^413

The gray image is a linear code over GF(7) with n=448, k=6 and d=367.
This code was found by Heurico 1.16 in 4.79 seconds.