The generator matrix

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

generates a code of length 11 over Z7[X]/(X^2) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+66x^56+132x^63+2058x^66+66x^70+78x^77

The gray image is a linear code over GF(7) with n=77, k=4 and d=56.
This code was found by Heurico 1.16 in 0.001 seconds.