The generator matrix

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

generates a code of length 35 over Z4 who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+28x^30+54x^32+48x^34+48x^36+48x^38+24x^40+4x^46+1x^64

The gray image is a code over GF(2) with n=70, k=8 and d=30.
This code was found by Heurico 1.16 in 0.0185 seconds.