The generator matrix

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

generates a code of length 11 over Z8 who´s minimum homogenous weight is 2.

Homogenous weight enumerator: w(x)=1x^0+23x^2+163x^4+597x^6+1338x^8+1536x^9+1974x^10+21504x^11+1974x^12+1536x^13+1338x^14+597x^16+163x^18+23x^20+1x^22

The gray image is a code over GF(2) with n=44, k=15 and d=4.
This code was found by Heurico 1.16 in 0.389 seconds.