The generator matrix

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

generates a code of length 50 over Z7[X]/(X^2) who´s minimum homogenous weight is 292.

Homogenous weight enumerator: w(x)=1x^0+3780x^292+1764x^293+114x^294+3024x^299+588x^300+138x^301+5544x^306+1764x^307+72x^308+18x^315

The gray image is a linear code over GF(7) with n=350, k=5 and d=292.
This code was found by Heurico 1.16 in 17.5 seconds.