The generator matrix

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

generates a code of length 49 over Z7[X]/(X^2) who´s minimum homogenous weight is 286.

Homogenous weight enumerator: w(x)=1x^0+4410x^286+966x^287+3528x^293+450x^294+6468x^300+972x^301+6x^308+6x^322

The gray image is a linear code over GF(7) with n=343, k=5 and d=286.
This code was found by Heurico 1.16 in 0.266 seconds.