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

generates a code of length 35 over Z4 who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+4x^34+22x^36+4x^38+1x^40

The gray image is a code over GF(2) with n=70, k=5 and d=34.
This code was found by Heurico 1.16 in 0.00424 seconds.