The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+33x^4+100x^5+167x^6+378x^7+675x^8+1448x^9+3255x^10+4310x^11+3171x^12+1508x^13+653x^14+358x^15+216x^16+80x^17+21x^18+10x^19

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 0.207 seconds.