The generator matrix

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

generates a code of length 49 over Z7[X]/(X^2) who´s minimum homogenous weight is 273.

Homogenous weight enumerator: w(x)=1x^0+222x^273+570x^280+432x^287+14718x^294+240x^301+228x^308+156x^315+138x^322+60x^329+30x^336+12x^343

The gray image is a linear code over GF(7) with n=343, k=5 and d=273.
This code was found by Heurico 1.16 in 0.23 seconds.