The generator matrix

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

generates a code of length 12 over Z7[X]/(X^2) who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+360x^49+1170x^56+2280x^63+14406x^66+5112x^70+86436x^73+5256x^77+2628x^84

The gray image is a linear code over GF(7) with n=84, k=6 and d=49.
This code was found by Heurico 1.16 in 1.29 seconds.