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

generates a code of length 52 over Z7[X]/(X^2) who´s minimum homogenous weight is 298.

Homogenous weight enumerator: w(x)=1x^0+2730x^298+4200x^299+1428x^300+30x^301+2520x^303+630x^304+13776x^305+11172x^306+3024x^307+120x^308+3780x^310+504x^311+15708x^312+12096x^313+2898x^314+150x^315+6048x^317+924x^318+19236x^319+13692x^320+2940x^321+6x^322+36x^329

The gray image is a linear code over GF(7) with n=364, k=6 and d=298.
This code was found by Heurico 1.16 in 3.69 seconds.