The generator matrix

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

generates a code of length 11 over Z7[X]/(X^2) who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+132x^49+462x^56+2058x^60+462x^63+12348x^67+924x^70+420x^77

The gray image is a linear code over GF(7) with n=77, k=5 and d=49.
This code was found by Heurico 1.16 in 0.028 seconds.