The generator matrix

 1  1  1  1  1  1  1  1  1  1  1
 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  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+11x^2+55x^4+165x^6+330x^8+462x^10+6144x^11+462x^12+330x^14+165x^16+55x^18+11x^20+1x^22

The gray image is a code over GF(2) with n=44, k=13 and d=4.
This code was found by Heurico 1.16 in 0.0319 seconds.