The generator matrix

 1  0  1
 0  1 5X+1
 0  0 5X

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+882x^12+108x^14+10290x^18+5292x^19+216x^21

The gray image is a linear code over GF(7) with n=21, k=5 and d=7.
This code was found by Heurico 1.16 in 0.00105 seconds.