The generator matrix

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

generates a code of length 8 over Z7[X]/(X^2) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+420x^28+1008x^35+4032x^42+100842x^48+6432x^49+4914x^56

The gray image is a linear code over GF(7) with n=56, k=6 and d=28.
This code was found by Heurico 1.16 in 0.376 seconds.