The generator matrix

 1  0  0  0  0  1  1  1  0  1  1  0  2  2  2  1
 0  1  0  0  0  0  0  0  0  1  1  1  2  2  0  0
 0  0  1  0  0  0  1  1  1  1  1  2  2  0  0  0
 0  0  0  1  0  1  1  0  1  0  1  3  1  1  1  0
 0  0  0  0  1  1  0  1  1  0  1  1  1  3  1  0
 0  0  0  0  0  2  0  0  0  0  2  2  2  0  2  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  0  2  0  2  2  2
 0  0  0  0  0  0  0  0  2  0  2  2  0  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+124x^8+144x^9+168x^10+344x^11+925x^12+1416x^13+1728x^14+2232x^15+2161x^16+2120x^17+1936x^18+1416x^19+850x^20+408x^21+256x^22+104x^23+34x^24+8x^25+8x^26+1x^28

The gray image is a code over GF(2) with n=32, k=14 and d=8.
This code was found by Heurico 1.16 in 2.63 seconds.