The generator matrix

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

generates a code of length 15 over Z4 who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+39x^6+141x^8+312x^10+1128x^12+2475x^14+2475x^16+1128x^18+312x^20+141x^22+39x^24+1x^30

The gray image is a code over GF(2) with n=30, k=13 and d=6.
This code was found by Heurico 1.16 in 16.4 seconds.