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

generates a code of length 52 over Z7[X]/(X^2) who´s minimum homogenous weight is 287.

Homogenous weight enumerator: w(x)=1x^0+168x^287+378x^293+1668x^294+378x^296+1554x^297+1722x^300+6012x^301+1806x^303+4158x^304+3150x^307+15954x^308+5544x^310+11718x^311+5544x^314+29400x^315+6678x^317+11382x^318+3612x^321+6312x^322+162x^329+162x^336+114x^343+42x^350+24x^357+6x^364

The gray image is a linear code over GF(7) with n=364, k=6 and d=287.
This code was found by Heurico 1.16 in 4.37 seconds.