The generator matrix

 1  0  1  1  1  0  1  1  2  1  1
 0  1  1  0  1  1  3  3  4  0  0
 0  0  2  0  0  0  6  0  0  4  0
 0  0  0  2  0  6  6  2  0  4  0
 0  0  0  0  2  0  6  2  2  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  0

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

Homogenous weight enumerator: w(x)=1x^0+70x^4+430x^6+416x^7+1864x^8+3456x^9+5806x^10+8640x^11+5890x^12+3456x^13+1786x^14+416x^15+487x^16+42x^18+8x^20

The gray image is a code over GF(2) with n=44, k=15 and d=8.
This code was found by Heurico 1.16 in 0.54 seconds.