The generator matrix

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

generates a code of length 12 over Z7[X]/(X^2) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+222x^56+432x^63+540x^70+14406x^72+840x^77+366x^84

The gray image is a linear code over GF(7) with n=84, k=5 and d=56.
This code was found by Heurico 1.16 in 0.033 seconds.