The generator matrix

 1  0  1  1  1  1  1  1  1  1  1
 0  1  3  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  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+8118x^10+12288x^11+8118x^12+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 0.296 seconds.