The generator matrix

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

generates a code of length 10 over Z7[X]/(X^2) who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+42x^49+144x^56+2058x^60+66x^63+90x^70

The gray image is a linear code over GF(7) with n=70, k=4 and d=49.
This code was found by Heurico 1.16 in 0.000891 seconds.