The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+82x^8+246x^10+995x^12+1644x^14+2249x^16+1672x^18+954x^20+276x^22+68x^24+2x^26+3x^28

The gray image is a code over GF(2) with n=32, k=13 and d=8.
This code was found by Heurico 1.16 in 0.406 seconds.