The generator matrix

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

generates a code of length 51 over Z7[X]/(X^2) who´s minimum homogenous weight is 287.

Homogenous weight enumerator: w(x)=1x^0+420x^287+42x^288+504x^294+756x^295+456x^301+4536x^302+228x^308+9072x^309+222x^315+174x^322+174x^329+138x^336+72x^343+6x^350+6x^357

The gray image is a linear code over GF(7) with n=357, k=5 and d=287.
This code was found by Heurico 1.16 in 7.99 seconds.