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

generates a code of length 39 over Z7[X]/(X^2) who´s minimum homogenous weight is 203.

Homogenous weight enumerator: w(x)=1x^0+576x^203+1296x^210+1770x^217+1980x^224+2616x^231+100842x^234+2736x^238+2736x^245+1938x^252+876x^259+270x^266+12x^273

The gray image is a linear code over GF(7) with n=273, k=6 and d=203.
This code was found by Heurico 1.16 in 8.06 seconds.