The generator matrix

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

generates a code of length 20 over Z4 who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+264x^14+478x^16+770x^18+996x^20+910x^22+472x^24+158x^26+36x^28+10x^30+1x^32

The gray image is a code over GF(2) with n=40, k=12 and d=14.
This code was found by Heurico 1.16 in 63.4 seconds.