The generator matrix

 1  1  1  1  1  1
 0  5  0  5 10 10
 0  0  5 15 10 15

generates a code of length 6 over Z25 who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+60x^20+500x^24+24x^25+40x^30

The gray image is a code over GF(5) with n=30, k=4 and d=20.
This code was found by Heurico 1.16 in -1.01e-007 seconds.