The generator matrix

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

generates a code of length 20 over Z4 who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+63x^16+84x^17+46x^18+48x^19+44x^20+72x^21+52x^22+16x^23+20x^24+36x^25+30x^26

The gray image is a code over GF(2) with n=40, k=9 and d=16.
This code was found by Heurico 1.10 in 0 seconds.