The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+487x^8+1668x^10+5344x^12+8912x^14+8871x^16+5208x^18+1904x^20+336x^22+33x^24+4x^26

The gray image is a code over GF(2) with n=30, k=15 and d=8.
This code was found by Heurico 1.10 in 643 seconds.