The generator matrix

 1  0  0  0  1  1  1  1  1  1  1
 0  1  0  0  1  2  0  5  0  1  0
 0  0  1  0  1  0  3  1  1  2  2
 0  0  0  1  1  3  0  2  3  3  3
 0  0  0  0  2  2  6  0  2  0  6
 0  0  0  0  0  4  0  0  4  4  0
 0  0  0  0  0  0  4  4  4  4  0

generates a code of length 11 over Z8 who´s minimum homogenous weight is 5.

Homogenous weight enumerator: w(x)=1x^0+42x^5+185x^6+872x^7+2825x^8+8038x^9+12341x^10+16916x^11+12363x^12+8022x^13+2827x^14+896x^15+170x^16+26x^17+7x^18+4x^19+1x^20

The gray image is a code over GF(2) with n=44, k=16 and d=10.
This code was found by Heurico 1.16 in 2.12 seconds.