The generator matrix
1 1 1 1 2 2 2 1 2 1 1
0 4 0 4 0 4 4 0 0 0 4
0 0 4 4 4 4 0 0 0 4 4
generates a code of length 11 over Z8 who´s minimum homogenous weight is 10.
Homogenous weight enumerator: w(x)=1x^0+3x^10+22x^11+3x^12+1x^14+2x^15
The gray image is a code over GF(2) with n=44, k=5 and d=20.
This code was found by Heurico 1.16 in 0.000321 seconds.