The generator matrix

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

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+180x^49+2058x^54+738x^56+12348x^61+1404x^63+78x^70

The gray image is a linear code over GF(7) with n=70, k=5 and d=49.
This code was found by Heurico 1.16 in 0.0117 seconds.