The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+33x^34+66x^35+68x^36+68x^37+48x^38+34x^39+33x^40+32x^41+25x^42+24x^43+20x^44+22x^45+16x^46+2x^47+4x^48+4x^49+4x^50+2x^51+2x^52+2x^53+2x^54

The gray image is a code over GF(2) with n=78, k=9 and d=34.
This code was found by Heurico 1.10 in 0 seconds.