The generator matrix

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

generates a code of length 11 over Z8 who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+3x^10+22x^11+3x^12+1x^14+2x^15

The gray image is a code over GF(2) with n=44, k=5 and d=20.
This code was found by Heurico 1.16 in 0.000321 seconds.