The generator matrix

 1  1  1  1  2  2  2  1  1  1  1
 0  2  0  2  0  2  2  0  0  0  0
 0  0  2  2  2  2  0  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

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

Homogenous weight enumerator: w(x)=1x^0+79x^4+168x^6+1346x^8+1536x^9+2376x^10+5120x^11+2838x^12+1536x^13+1016x^14+333x^16+24x^18+11x^20

The gray image is a code over GF(2) with n=44, k=14 and d=8.
This code was found by Heurico 1.16 in 0.216 seconds.