The generator matrix

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

generates a code of length 20 over Z4 who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+142x^10+699x^12+1838x^14+3874x^16+6314x^18+7166x^20+5984x^22+4096x^24+1862x^26+655x^28+114x^30+21x^32+2x^34

The gray image is a code over GF(2) with n=40, k=15 and d=10.
This code was found by Heurico 1.10 in 3.82 seconds.