The generator matrix

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

generates a code of length 11 over Z7[X]/(X^2) who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+198x^42+1032x^49+1812x^56+14406x^60+5202x^63+86436x^67+5442x^70+3120x^77

The gray image is a linear code over GF(7) with n=77, k=6 and d=42.
This code was found by Heurico 1.16 in 0.902 seconds.