The generator matrix

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

generates a code of length 50 over Z7[X]/(X^2) who´s minimum homogenous weight is 286.

Homogenous weight enumerator: w(x)=1x^0+1890x^286+4044x^287+2772x^288+462x^290+3318x^291+1806x^292+7014x^293+10656x^294+5502x^295+1428x^297+5124x^298+1680x^299+9114x^300+14070x^301+7140x^302+2226x^304+8022x^305+2688x^306+10794x^307+12660x^308+5166x^309+48x^315+12x^322+6x^336+6x^343

The gray image is a linear code over GF(7) with n=350, k=6 and d=286.
This code was found by Heurico 1.16 in 3.45 seconds.