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

generates a code of length 52 over Z7[X]/(X^2) who´s minimum homogenous weight is 294.

Homogenous weight enumerator: w(x)=1x^0+360x^294+588x^301+468x^308+14406x^312+420x^315+216x^322+66x^329+30x^336+48x^343+132x^350+54x^357+18x^364

The gray image is a linear code over GF(7) with n=364, k=5 and d=294.
This code was found by Heurico 1.16 in 12.7 seconds.