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  2  1  1  2  1  1  1  1
 0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  0  2  2  2  2  2  2
 0  0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  0  2  2  2  2  2
 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  0  2  2  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  2  0  0  2  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  2  2  2  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  0  2  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  2  2  2  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  2  0  0  2  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  0  2  2  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  0  2  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  0  2  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+424x^16+176x^20+2157x^24+4944x^28+6745x^32+848x^36+866x^40+176x^44+46x^48+1x^56

The gray image is a code over GF(2) with n=60, k=14 and d=16.
This code was found by Heurico 1.16 in 8.19 seconds.