The generator matrix

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

generates a code of length 20 over Z4 who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+225x^12+786x^14+1919x^16+3136x^18+4146x^20+3300x^22+1946x^24+688x^26+205x^28+26x^30+6x^32

The gray image is a code over GF(2) with n=40, k=14 and d=12.
This code was found by Heurico 1.16 in 6.93 seconds.