The generator matrix
1 1 1 1 1 1 1 2 2 2 1 1 1 1
0 4 0 4 0 0 4 0 4 4 4 0 0 4
0 0 4 4 0 4 4 4 4 0 0 0 4 4
generates a code of length 14 over Z8 who´s minimum homogenous weight is 13.
Homogenous weight enumerator: w(x)=1x^0+6x^13+19x^14+3x^16+2x^17+1x^22
The gray image is a code over GF(2) with n=56, k=5 and d=26.
This code was found by Heurico 1.16 in 0.000573 seconds.