The generator matrix

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

generates a code of length 15 over Z25 who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+40x^55+556x^60+12x^65+8x^70+8x^75

The gray image is a code over GF(5) with n=75, k=4 and d=55.
This code was found by Heurico 1.16 in 1.01e-007 seconds.