The generator matrix

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

generates a code of length 32 over Z8 who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+14x^34+1x^36

The gray image is a code over GF(2) with n=128, k=4 and d=68.
This code was found by Heurico 1.16 in 0.00764 seconds.