The generator matrix

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

generates a code of length 16 over Z4 who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+16x^12+38x^13+33x^14+24x^15+35x^16+36x^17+23x^18+24x^19+12x^20+6x^21+7x^22+1x^26

The gray image is a code over GF(2) with n=32, k=8 and d=12.
This code was found by Heurico 1.16 in 0.00184 seconds.