The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+55x^8+118x^12+128x^14+415x^16+128x^18+132x^20+41x^24+6x^28

The gray image is a code over GF(2) with n=32, k=10 and d=8.
This code was found by Heurico 1.16 in 0.00812 seconds.