The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  2  2
 0  2  0  0  0  0  0  0  0  0  0  0  0  2  2  2  0  2  2  2
 0  0  2  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  0  0
 0  0  0  2  0  0  0  0  0  0  2  2  2  0  2  2  0  0  2  2
 0  0  0  0  2  0  0  0  0  0  2  0  2  0  2  0  2  2  0  2
 0  0  0  0  0  2  0  0  0  2  0  0  2  0  0  2  2  2  2  2
 0  0  0  0  0  0  2  0  0  2  0  2  0  2  0  0  2  2  0  2
 0  0  0  0  0  0  0  2  0  2  2  2  0  2  0  2  0  2  2  0
 0  0  0  0  0  0  0  0  2  2  2  0  0  2  2  2  2  0  0  2

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

Homogenous weight enumerator: w(x)=1x^0+80x^14+162x^16+128x^18+192x^20+288x^22+152x^24+16x^30+5x^32

The gray image is a code over GF(2) with n=40, k=10 and d=14.
This code was found by Heurico 1.16 in 0.683 seconds.