The generator matrix

 1  0  0  0  1  1  1  2  0  0  1  1  1  0  1  2  2  0  1  2  1  0  1  2  1
 0  1  0  0  0  1  1  1  1  2  2  3  2  2  3  0  1  1  2  1  0  1  0  0  3
 0  0  1  0  1  1  0  3  2  1  0  1  1  2  2  1  0  3  1  1  3  0  1  1  0
 0  0  0  1  1  0  1  1  2  0  1  3  0  1  0  3  2  2  3  2  2  2  1  2  2
 0  0  0  0  2  0  2  0  2  2  2  2  2  0  0  0  2  0  0  2  0  0  0  2  0
 0  0  0  0  0  2  2  2  2  0  0  0  2  2  0  0  0  0  2  2  2  2  2  0  2

generates a code of length 25 over Z4 who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+144x^20+188x^22+197x^24+184x^26+169x^28+100x^30+30x^32+8x^34+3x^36

The gray image is a code over GF(2) with n=50, k=10 and d=20.
This code was found by Heurico 1.16 in 0.0607 seconds.