The generator matrix

 1  0  0  1  1  1  2  4  4  1  1
 0  1  0  1  2  7  1  0  0  4  7
 0  0  1  1  1  0  1  1  1  6  4
 0  0  0  2  0  6  4  6  2  2  0
 0  0  0  0  4  4  4  0  4  0  4

generates a code of length 11 over Z8 who´s minimum homogenous weight is 7.

Homogenous weight enumerator: w(x)=1x^0+72x^7+191x^8+484x^9+704x^10+1184x^11+711x^12+504x^13+176x^14+56x^15+8x^16+4x^17+1x^20

The gray image is a code over GF(2) with n=44, k=12 and d=14.
This code was found by Heurico 1.16 in 0.0345 seconds.