The generator matrix

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

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+588x^36+8568x^42+7056x^43+28812x^48+50448x^49+21168x^50+672x^56

The gray image is a linear code over GF(7) with n=56, k=6 and d=35.
This code was found by Heurico 1.16 in 0.203 seconds.