The generator matrix

 1  0  0  0  1  1  1  2  1  1  0  1  1  2  0  1  2  2  1  1  2  1  0  1  0  1  2  0  0  2  1  0  1  1  1  1  1  2  0
 0  1  0  0  0  0  2  0  1  1  1  3  3  1  1  2  1  1  2  0  1  0  1  1  2  1  2  2  2  0  1  0  3  1  1  0  3  2  1
 0  0  1  0  0  1  1  1  1  2  3  0  3  3  2  2  0  3  0  3  2  3  1  3  1  1  1  1  0  2  2  2  2  0  0  0  1  0  0
 0  0  0  1  1  3  0  1  2  3  3  2  3  0  1  3  1  0  0  1  2  2  3  2  1  1  3  1  1  1  0  1  1  1  3  0  3  1  0
 0  0  0  0  2  2  0  2  0  2  2  0  2  0  2  0  0  2  2  0  2  2  0  0  0  2  0  2  0  0  0  0  2  2  0  2  0  2  0

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

Homogenous weight enumerator: w(x)=1x^0+68x^34+128x^36+116x^38+66x^40+37x^42+33x^44+30x^46+23x^48+5x^50+5x^52

The gray image is a code over GF(2) with n=78, k=9 and d=34.
This code was found by Heurico 1.16 in 0.0254 seconds.