The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+134x^4+1134x^6+224x^7+4488x^8+5248x^9+14702x^10+13632x^11+14786x^12+5248x^13+4410x^14+224x^15+1191x^16+106x^18+8x^20

The gray image is a code over GF(2) with n=44, k=16 and d=8.
This code was found by Heurico 1.16 in 1.67 seconds.