The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  5  0  5 10 10  0  5 10 20 20 10 20  0
 0  0  5 15 10 15 10  5  5 15  0 20 20  5

generates a code of length 14 over Z25 who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+36x^50+48x^55+500x^56+24x^60+16x^70

The gray image is a code over GF(5) with n=70, k=4 and d=50.
This code was found by Heurico 1.16 in -1.01e-007 seconds.