The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+76x^4+40x^5+273x^6+304x^7+758x^8+984x^9+2988x^10+5536x^11+2988x^12+984x^13+758x^14+304x^15+273x^16+40x^17+76x^18+1x^22

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 0.193 seconds.