The generator matrix

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

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+942x^280+42x^282+168x^283+1554x^285+1344x^286+4944x^287+756x^289+1260x^290+4158x^292+2142x^293+8160x^294+4536x^296+5208x^297+11718x^299+6090x^300+18480x^301+9072x^303+7770x^304+11382x^306+4830x^307+12540x^308+168x^315+180x^322+84x^329+72x^336+48x^343

The gray image is a linear code over GF(7) with n=350, k=6 and d=280.
This code was found by Heurico 1.16 in 4.42 seconds.