The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  2  2  2  2  2  2  0  0  0  0  0  0
 0  2  0  0  0  2  2  2  0  0  0  2  0  2  2  2  0  0  2  0  2  2  2  0  2  2  2  2  0  0
 0  0  2  0  2  2  2  0  0  0  2  2  2  2  0  0  0  2  2  2  2  0  0  0  0  0  2  2  2  2
 0  0  0  2  2  0  2  2  0  2  2  0  0  2  2  0  2  2  0  0  2  2  0  0  0  2  2  0  0  2

generates a code of length 30 over Z4 who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+16x^30+15x^32

The gray image is a code over GF(2) with n=60, k=5 and d=30.
This code was found by Heurico 1.16 in 0.00252 seconds.