The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+68x^10+74x^11+210x^12+270x^13+433x^14+660x^15+938x^16+1298x^17+1535x^18+1784x^19+1817x^20+1818x^21+1542x^22+1264x^23+925x^24+702x^25+465x^26+246x^27+193x^28+72x^29+52x^30+4x^31+12x^32+1x^38

The gray image is a code over GF(2) with n=40, k=14 and d=10.
This code was found by Heurico 1.10 in 1.22 seconds.