The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+121x^4+116x^5+737x^6+1034x^7+2677x^8+6080x^9+12857x^10+18318x^11+12829x^12+6052x^13+2683x^14+1062x^15+750x^16+104x^17+107x^18+2x^19+6x^20

The gray image is a code over GF(2) with n=44, k=16 and d=8.
This code was found by Heurico 1.16 in 2.03 seconds.