The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+44x^4+49x^6+214x^8+512x^9+204x^10+2048x^11+204x^12+512x^13+214x^14+49x^16+44x^18+1x^22

The gray image is a code over GF(2) with n=44, k=12 and d=8.
This code was found by Heurico 1.16 in 0.0126 seconds.