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

generates a code of length 51 over Z7[X]/(X^2) who´s minimum homogenous weight is 273.

Homogenous weight enumerator: w(x)=1x^0+612x^273+1356x^280+1608x^287+2058x^294+2214x^301+100842x^306+2328x^308+2220x^315+1956x^322+1350x^329+858x^336+216x^343+24x^350+6x^357

The gray image is a linear code over GF(7) with n=357, k=6 and d=273.
This code was found by Heurico 1.16 in 17 seconds.