The generator matrix

 1  0  0  1  1  1  0  1  1  0  1  1  0  2  2
 0  1  0  1  0  1  1  0  0  0  1  3  1  1  0
 0  0  1  1  1  0  1  0  1  1  1  0  0  1  0
 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  2  0
 0  0  0  0  0  2  0  0  0  0  2  2  2  0  0
 0  0  0  0  0  0  2  0  0  0  2  2  2  2  2
 0  0  0  0  0  0  0  2  0  0  2  0  0  2  2
 0  0  0  0  0  0  0  0  2  0  0  2  0  2  2
 0  0  0  0  0  0  0  0  0  2  2  0  2  2  0

generates a code of length 15 over Z4 who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+161x^8+392x^10+1456x^12+1960x^14+2395x^16+1176x^18+560x^20+56x^22+35x^24

The gray image is a code over GF(2) with n=30, k=13 and d=8.
This code was found by Heurico 1.16 in 11.3 seconds.