The generator matrix

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

generates a code of length 21 over Z4 who´s minimum homogenous weight is 11.

Homogenous weight enumerator: w(x)=1x^0+70x^11+201x^12+420x^13+780x^14+1438x^15+2572x^16+3684x^17+4951x^18+6806x^19+8026x^20+8040x^21+7504x^22+6556x^23+5268x^24+3832x^25+2478x^26+1458x^27+805x^28+404x^29+156x^30+54x^31+23x^32+4x^33+3x^34+2x^35

The gray image is a code over GF(2) with n=42, k=16 and d=11.
This code was found by Heurico 1.10 in 24.3 seconds.