The generator matrix

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

generates a code of length 16 over Z4 who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+179x^8+980x^10+3474x^12+7168x^14+9095x^16+7304x^18+3436x^20+928x^22+197x^24+4x^26+2x^28

The gray image is a code over GF(2) with n=32, k=15 and d=8.
This code was found by Heurico 1.16 in 4.7 seconds.