The generator matrix

 1  0  1  1  1  1  1
 0  1 3X+1  2 3X+4  3  X

generates a code of length 7 over Z5[X]/(X^2) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+100x^24+44x^25+400x^29+80x^30

The gray image is a linear code over GF(5) with n=35, k=4 and d=24.
This code was found by Heurico 1.16 in 0.000127 seconds.