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

generates a code of length 58 over Z7[X]/(X^2) who´s minimum homogenous weight is 341.

Homogenous weight enumerator: w(x)=1x^0+882x^341+90x^343+294x^348+210x^350+882x^355+42x^357

The gray image is a linear code over GF(7) with n=406, k=4 and d=341.
This code was found by Heurico 1.16 in 0.0492 seconds.