The generator matrix
1 0 1 1
0 1 5X+1 3
generates a code of length 4 over Z7[X]/(X^2) who´s minimum homogenous weight is 18.
Homogenous weight enumerator: w(x)=1x^0+168x^18+24x^21+1176x^24+1008x^25+24x^28
The gray image is a linear code over GF(7) with n=28, k=4 and d=18.
This code was found by Heurico 1.16 in 9.99e-005 seconds.