The generator matrix

 1  1  1  1  1  1  2  1  1  1  1
 0  2  0  0  0  0  0  2  0  4  0
 0  0  2  0  0  0  0  2  0  6  4
 0  0  0  2  0  0  2  0  0  4  4
 0  0  0  0  2  0  2  2  2  6  0
 0  0  0  0  0  2  2  2  2  0  4
 0  0  0  0  0  0  4  0  4  4  4
 0  0  0  0  0  0  0  4  4  4  0

generates a code of length 11 over Z8 who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+35x^4+116x^5+308x^6+636x^7+1150x^8+2052x^9+6708x^10+10764x^11+6682x^12+2076x^13+1148x^14+628x^15+321x^16+108x^17+28x^18+4x^19+3x^20

The gray image is a code over GF(2) with n=44, k=15 and d=8.
This code was found by Heurico 1.16 in 0.77 seconds.