The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+108x^14+273x^16+392x^18+485x^20+432x^22+254x^24+88x^26+10x^28+4x^30+1x^36

The gray image is a code over GF(2) with n=40, k=11 and d=14.
This code was found by Heurico 1.16 in 81.1 seconds.