The generator matrix

 1  1  1  1  1  1  1
 0  X  0  X 3X 6X 6X
 0  0  X 5X 3X  X 3X

generates a code of length 7 over Z7[X]/(X^2) who´s minimum homogenous weight is 35.

Homogenous weight enumerator: w(x)=1x^0+126x^35+2142x^42+132x^49

The gray image is a linear code over GF(7) with n=49, k=4 and d=35.
This code was found by Heurico 1.16 in 0.000382 seconds.