The generator matrix

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

generates a code of length 30 over Z4 who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+506x^16+1288x^24+253x^28+4096x^30+253x^32+1288x^36+506x^44+1x^60

The gray image is a code over GF(2) with n=60, k=13 and d=16.
This code was found by Heurico 1.16 in 4.42 seconds.