The generator matrix

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

generates a code of length 20 over Z4 who´s minimum homogenous weight is 11.

Homogenous weight enumerator: w(x)=1x^0+72x^11+200x^12+410x^13+710x^14+1164x^15+1871x^16+2576x^17+3327x^18+3916x^19+4118x^20+4060x^21+3430x^22+2540x^23+1824x^24+1200x^25+704x^26+364x^27+178x^28+74x^29+20x^30+8x^31+1x^34

The gray image is a code over GF(2) with n=40, k=15 and d=11.
This code was found by Heurico 1.10 in 5.3 seconds.