The generator matrix

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

generates a code of length 39 over Z4 who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+48x^30+80x^31+139x^32+206x^33+242x^34+258x^35+319x^36+304x^37+282x^38+320x^39+314x^40+356x^41+300x^42+284x^43+194x^44+144x^45+132x^46+80x^47+48x^48+14x^49+18x^50+2x^51+7x^52+2x^54+2x^56

The gray image is a code over GF(2) with n=78, k=12 and d=30.
This code was found by Heurico 1.16 in 1.11 seconds.