The generator matrix

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

generates a code of length 51 over Z7[X]/(X^2) who´s minimum homogenous weight is 292.

Homogenous weight enumerator: w(x)=1x^0+2730x^292+2814x^293+3300x^294+378x^295+504x^296+1260x^297+1218x^298+12138x^299+7182x^300+6378x^301+1890x^302+1344x^303+1890x^304+1092x^305+14868x^306+7770x^307+6942x^308+3906x^309+2268x^310+3024x^311+1806x^312+17598x^313+8988x^314+6312x^315+18x^322+12x^329+18x^336

The gray image is a linear code over GF(7) with n=357, k=6 and d=292.
This code was found by Heurico 1.16 in 3.53 seconds.