The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+236x^12+634x^14+1911x^16+3240x^18+4373x^20+3148x^22+1986x^24+648x^26+190x^28+10x^30+6x^32+1x^36

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 6.28 seconds.