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

generates a code of length 50 over Z7[X]/(X^2) who´s minimum homogenous weight is 266.

Homogenous weight enumerator: w(x)=1x^0+498x^266+1146x^273+1686x^280+1962x^287+2058x^288+2196x^294+24696x^295+2256x^301+74088x^302+2316x^308+2082x^315+1572x^322+834x^329+192x^336+60x^343+6x^350

The gray image is a linear code over GF(7) with n=350, k=6 and d=266.
This code was found by Heurico 1.16 in 10.6 seconds.