The generator matrix

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

generates a code of length 15 over Z4 who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+66x^4+507x^8+1144x^12+2048x^14+3335x^16+858x^20+221x^24+12x^28

The gray image is a code over GF(2) with n=30, k=13 and d=4.
This code was found by Heurico 1.16 in 0.394 seconds.