The generator matrix

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

generates a code of length 4 over Z7[X]/(X^2) who´s minimum homogenous weight is 7.

Homogenous weight enumerator: w(x)=1x^0+24x^7+294x^12+216x^14+4116x^18+3528x^19+864x^21+72030x^24+24696x^25+10584x^26+1296x^28

The gray image is a linear code over GF(7) with n=28, k=6 and d=7.
This code was found by Heurico 1.16 in 0.0493 seconds.