The generator matrix

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

generates a code of length 16 over Z4 who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+58x^14+27x^16+28x^18+4x^20+10x^22

The gray image is a code over GF(2) with n=32, k=7 and d=14.
This code was found by Heurico 1.16 in 0.0217 seconds.