The generator matrix

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

generates a code of length 11 over Z8 who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+43x^6+149x^8+192x^9+307x^10+640x^11+339x^12+192x^13+153x^14+22x^16+9x^18+1x^20

The gray image is a code over GF(2) with n=44, k=11 and d=12.
This code was found by Heurico 1.16 in 0.00875 seconds.