The generator matrix

 1  1  1
 0  X  0
 0  0  X

generates a code of length 3 over Z7[X]/(X^2) who´s minimum homogenous weight is 7.

Homogenous weight enumerator: w(x)=1x^0+18x^7+108x^14+2058x^18+216x^21

The gray image is a linear code over GF(7) with n=21, k=4 and d=7.
This code was found by Heurico 1.16 in 7.51e-005 seconds.