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

generates a code of length 50 over Z7[X]/(X^2) who´s minimum homogenous weight is 280.

Homogenous weight enumerator: w(x)=1x^0+360x^280+426x^287+456x^294+14406x^300+378x^301+228x^308+198x^315+132x^322+90x^329+96x^336+24x^343+12x^350

The gray image is a linear code over GF(7) with n=350, k=5 and d=280.
This code was found by Heurico 1.16 in 0.232 seconds.