The generator matrix

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

generates a code of length 8 over Z7[X]/(X^2) who´s minimum homogenous weight is 35.

Homogenous weight enumerator: w(x)=1x^0+336x^35+2394x^42+13404x^49+672x^56

The gray image is a linear code over GF(7) with n=56, k=5 and d=35.
This code was found by Heurico 1.16 in 0.0118 seconds.