The generator matrix

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

generates a code of length 4 over Z7[X]/(X^2) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+252x^12+36x^14+5880x^18+3024x^19+120x^21+63798x^24+35280x^25+9072x^26+186x^28

The gray image is a linear code over GF(7) with n=28, k=6 and d=12.
This code was found by Heurico 1.16 in 0.0456 seconds.