The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+89x^8+596x^10+1576x^12+3520x^14+4707x^16+3592x^18+1752x^20+480x^22+67x^24+4x^26

The gray image is a code over GF(2) with n=32, k=14 and d=8.
This code was found by Heurico 1.10 in 0.638 seconds.