The generator matrix

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

generates a code of length 28 over Z8 who´s minimum homogenous weight is 29.

Homogenous weight enumerator: w(x)=1x^0+8x^29+5x^30+1x^32+1x^34

The gray image is a code over GF(2) with n=112, k=4 and d=58.
This code was found by Heurico 1.16 in 0.00474 seconds.