The generator matrix

 1  0  0  0  0  0  0  1  1  2  1  0  2  0  1  1
 0  1  0  0  0  0  0  0  1  0  1  1  2  0  3  2
 0  0  1  0  0  0  0  2  1  1  3  0  1  1  3  2
 0  0  0  1  0  0  0  3  0  0  3  2  3  2  0  0
 0  0  0  0  1  0  0  1  2  3  3  3  3  2  1  0
 0  0  0  0  0  1  0  1  3  1  2  1  2  1  3  0
 0  0  0  0  0  0  1  1  1  2  0  2  3  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+45x^8+150x^9+256x^10+454x^11+843x^12+1314x^13+1754x^14+2198x^15+2353x^16+2142x^17+1842x^18+1314x^19+804x^20+486x^21+238x^22+130x^23+49x^24+4x^25+6x^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 4.3 seconds.