The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+68x^4+128x^5+224x^6+384x^7+638x^8+1792x^9+2120x^10+5632x^11+2204x^12+1792x^13+560x^14+384x^15+281x^16+128x^17+40x^18+8x^20

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 0.11 seconds.