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

generates a code of length 39 over Z4 who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+28x^34+54x^36+54x^38+52x^40+38x^42+16x^44+2x^46+3x^48+6x^50+1x^52+1x^68

The gray image is a code over GF(2) with n=78, k=8 and d=34.
This code was found by Heurico 1.16 in 3.28 seconds.