The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+44x^11+127x^12+276x^13+517x^14+798x^15+1209x^16+1894x^17+2642x^18+3300x^19+3796x^20+3736x^21+3553x^22+3344x^23+2580x^24+1876x^25+1366x^26+800x^27+469x^28+276x^29+113x^30+34x^31+10x^32+6x^33+1x^38

The gray image is a code over GF(2) with n=42, k=15 and d=11.
This code was found by Heurico 1.10 in 5.22 seconds.