The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+66x^14+96x^15+146x^16+192x^17+184x^18+208x^19+228x^20+256x^21+204x^22+192x^23+124x^24+64x^25+56x^26+16x^27+12x^28+2x^30+1x^32

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 0.132 seconds.