The generator matrix

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

generates a code of length 52 over Z7[X]/(X^2) who´s minimum homogenous weight is 301.

Homogenous weight enumerator: w(x)=1x^0+72x^301+252x^302+420x^303+1260x^304+882x^305+3150x^306+144x^308+672x^309+630x^310+1008x^311+294x^312+756x^313+48x^315+1134x^316+1008x^317+1848x^318+882x^319+2268x^320+18x^322+30x^329+18x^336+6x^343+6x^350

The gray image is a linear code over GF(7) with n=364, k=5 and d=301.
This code was found by Heurico 1.16 in 96 seconds.