The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  2  2  2  2  2  0  1  1  1  0  0  0  0  0  0  1
 0  2  0  0  0  2  2  2  0  0  0  2  0  2  2  2  0  0  2  0  2  2  2  2  0  0  0  2  2  2  0  0  0  2
 0  0  2  0  2  2  2  0  0  0  2  2  2  2  0  0  0  2  2  2  2  0  0  0  0  0  2  0  2  2  2  2  0  2
 0  0  0  2  2  0  2  2  0  2  2  0  0  2  2  0  2  2  0  0  2  2  0  0  0  2  2  2  2  0  0  2  2  0

generates a code of length 34 over Z4 who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+20x^34+6x^36+4x^38+1x^40

The gray image is a code over GF(2) with n=68, k=5 and d=34.
This code was found by Heurico 1.16 in 0.00782 seconds.